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Journal articles on the topic 'Q-integral operator'

Author: Grafiati
Published: 7 June 2025
Last updated: 17 July 2025

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1

Momenzadeh, M., and N. I. Mahmudov. "Study of new class of q-fractional integral operator." Filomat 33, no. 17 (2019): 5713–21. http://dx.doi.org/10.2298/fil1917713m.

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In this paper, we study on the new class of q-fractional integral operator. In the aid of iterated Cauchy integral approach to fractional integral operator, we applied tp f(t) in these integrals and a new class of q-fractional integral operator with parameter p, is introduced. Recently, the q-analogue of fractional differential integral operator is studied and all of the operators defined in these studies are q-analogue of Riemann fractional differential operator. We show that our new class of operator generalize all the operators in use, and additionally, it can cover the q-analogue of Hadamard fractional differential operator, as well. Some properties of this operator are investigated.
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2

Aglić Aljinović, Andrea, Ilko Brnetić, and Ana Žgaljić Keko. "Triangle inequality for quantum integral operator." Acta mathematica Spalatensia 2 (December 1, 2022): 97–110. http://dx.doi.org/10.32817/ams.2.7.

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We show that general integral triangle inequality does not hold for shifted q-integrals. Furthermore, we obtain a triangle inequality for shifted qintegrals. We also give an estimate for q-integrable product and use it to refine some recently obtained Ostrowski inequalities for quantum calculus.
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3

Saad, Husam L. "Applications of the Operator _r Φ_s in q-Integrals". BASRA JOURNAL OF SCIENCE 40, № 3 (2022): 526–41. http://dx.doi.org/10.29072/basjs.20220301.

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We establish general q -operator rQs and subsequently discover some of its operator identities, which we use to generalize various q-integrals such as the Andrews-Askey integral, Gasper integral, and Askey-Wilson integral. In -integrals, we specify exact values for achieving certain new results or reproofing others.
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4

Al-Shaikh, Suha B., Ahmad A. Abubaker, Khaled Matarneh, and Mohammad Faisal Khan. "Some New Applications of the q-Analogous of Differential and Integral Operators for New Subclasses of q-Starlike and q-Convex Functions." Fractal and Fractional 7, no. 5 (2023): 411. http://dx.doi.org/10.3390/fractalfract7050411.

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In the geometric function theory of complex analysis, the investigation of the geometric properties of analytic functions using q-analogues of differential and integral operators is an important area of study, offering powerful tools for applications in numerical analysis and the solution of differential equations. Many topics, including complex analysis, hypergeometric series, and particle physics, have been generalized in q-calculus. In this study, first of all, we define the q-analogues of a differential operator (DRλ,qm,n) by using the basic idea of q-calculus and the definition of convolution. Additionally, using the newly constructed operator (DRλ,qm,n), we establish the q-analogues of two new integral operators (Fλ,γ1,γ2,…γlm,n,q and Gλ,γ1,γ2,…γlm,n,q), and by employing these operators, new subclasses of the q-starlike and q-convex functions are defined. Sufficient conditions for the functions (f) that belong to the newly defined classes are investigated. Additionally, certain subordination findings for the differential operator (DRλ,qm,n) and novel geometric characteristics of the q-analogues of the integral operators in these classes are also obtained. Our results are generalizations of results that were previously proven in the literature.
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5

Al-Omari, Shrideh, Wael Salameh, and Sharifah Alhazmi. "Notes on q-Gamma Operators and Their Extension to Classes of Generalized Distributions." Symmetry 16, no. 10 (2024): 1294. http://dx.doi.org/10.3390/sym16101294.

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This paper discusses definitions and properties of q-analogues of the gamma integral operator and its extension to classes of generalized distributions. It introduces q-convolution products, symmetric q-delta sequences and q-quotients of sequences, and establishes certain convolution theorems. The convolution theorems are utilized to accomplish q-equivalence classes of generalized distributions called q-Boehmians. Consequently, the q-gamma operators are therefore extended to the generalized spaces and performed to coincide with the classical integral operator. Further, the generalized q-gamma integral is shown to be linear, sequentially continuous and continuous with respect to some involved convergence equipped with the generalized spaces.
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6

Al-Omari, Shrideh, Wael Salameh, and Hamzeh Zureigat. "Convolution Theorem for p,q-Gamma Integral Transforms and Their Application to Some Special Functions." Symmetry 16, no. 7 (2024): 882. http://dx.doi.org/10.3390/sym16070882.

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This article introduces (p,q)-analogs of the gamma integral operator and discusses their expansion to power functions, (p,q)-exponential functions, and (p,q)-trigonometric functions. Additionally, it validates other findings concerning (p,q)-analogs of the gamma integrals to unit step functions as well as first- and second-order (p,q)-differential operators. In addition, it presents a pair of (p,q)-convolution products for the specified (p,q)-analogs and establishes two (p,q)-convolution theorems.
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7

Al-Omari, Shrideh, Wael Salameh, and Sharifah Alhazmi. "Some Estimates for Certain q-analogs of Gamma Integral Transform Operators." Symmetry 16, no. 10 (2024): 1368. http://dx.doi.org/10.3390/sym16101368.

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The aim of this work is to examine some q-analogs and differential properties of the gamma integral operator and its convolution products. The q-gamma integral operator is introduced in two versions in order to derive pertinent conclusions regarding the q-exponential functions. Also, new findings on the q-trigonometric, q-sine, and q-cosine functions are extracted. In addition, novel results for first and second-order q-differential operators are established and extended to Heaviside unit step functions. Lastly, three crucial convolution products and extensive convolution theorems for the q-analogs are also provided.
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8

Chana, Ahmed, and Abdellatif Akhlidj. "Uncertainty Principles and Extremal Functions for Bessel Multiplier Operators in Quantum Calculus." European Journal of Mathematical Analysis 5 (April 1, 2025): 8. https://doi.org/10.28924/ada/ma.5.8.

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Using the q-Jackson integral and some elements of the q-harmonic analysis associated with the q-Bessel operator for fixed 0 < q < 1, we introduce the q-Bessel multiplier operators and we give some new results related to these operators as Plancherel’s, Calderón’s reproducing formulas and Heisenberg’s, Donoho-Stark’s uncertainty principles. Next, using the theory of reproducing kernels we give best estimates and an integral representation of the extremal functions related to these operators on weighted Sobolev spaces.
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9

Chana, Ahmed, and Abdellatif Akhlidj. "Best approximate inversion formulas for Quantum Bessel multiplier operators." Open Journal of Mathematical Sciences 9 (February 27, 2025): 1–13. https://doi.org/10.30538/oms2025.0239.

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Using the \(q\)-Jackson integral and some elements of the \(q\)-harmonic analysis associated with the generalized q-Bessel operator for fixed \(0<q<1\), we introduce the generalized q-Bessel multiplier operators and we give some new results related to these operators as Plancherel’s, Calderón's reproducing formulas and Heisenberg's, Donoho-Stark's uncertainty principles. Next, using the theory of reproducing kernels we give best estimates and an integral representation of the extremal functions related to these operators on weighted Sobolev spaces.
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10

Aglic-Aljinovic, Andrea, Domagoj Kovacevic, Mate Puljiz, and Ana Zgaljic-Keko. "Sharp trapezoid inequality for quantum integral operator." Filomat 36, no. 16 (2022): 5653–64. http://dx.doi.org/10.2298/fil2216653a.

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Trapezoid inequality estimates the difference of the integral mean of a function on the finite interval [a, b] and the arithmetic mean of its values at the endpoints a and b. Quantum calculus is the calculus based on finite diference principle or without the concept of limits. Euler-Jackson q-difference operator and q-integral operator are discretization of ordinary derivatives and integrals and they can be generalized to its shifted versions on arbitrary domain [a, b]. In this paper we disprove a trapezoid inequality for shifted quantum integral operator appearing in the literature by giving two counterexamples. We point out some differences between the definite q-integral and Riemann integral to explain why the mistake is made and obtain corrected results. We also prove the sharpness of our new bounds in estimating the value of the quantum integral mean. Further we derive generalized sharp trapezoid inequality in which we point out the case with tightest bounds.
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11

Badar, Rizwan Salim, and Khalida Inayat Noor. "Generalized q-Srivastava-Attiya operator on multivalent functions." Studia Universitatis Babes-Bolyai Matematica 69, no. 1 (2024): 75–82. http://dx.doi.org/10.24193/subbmath.2024.1.05.

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In this article, we define a generalized q-integral operator on multivalent functions. It generalizes many known linear operators in Geometric Function Theory (GFT). Inclusions results, convolution properties and q-Bernardi integral preservation of the subclasses of analytic functions are discussed. Mathematics Subject Classification (2010): 30C45, 30C80, 30H05. Received 29 March 2021; Accepted 26 July 2021
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12

Fardi, Mojtaba, Ebrahim Amini, and Shrideh Al-Omari. "On Certain Analogues of Noor Integral Operators Associated with Fractional Integrals." Journal of Function Spaces 2024 (January 22, 2024): 1–11. http://dx.doi.org/10.1155/2024/4565581.

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In this paper, we employ a q-Noor integral operator to perform a q-analogue of certain fractional integral operator defined on an open unit disc. Then, we make use of the Hadamard convolution product to discuss several related results. Also, we derive a class of convex functions by utilizing the q-fractional integral operator and apply the inspired presented theory of the differential subordination, to geometrically explore the most popular differential subordination properties of the aforementioned operator. In addition, we discuss an exciting inclusion for the given convex class of functions. Over and above, we investigate the q-fractional integral operator and obtain some applications for the differential subordination.
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13

Al-Shbeil, Isra, Jianhua Gong, Samrat Ray, Shahid Khan, Nazar Khan, and Hala Alaqad. "The Properties of Meromorphic Multivalent q-Starlike Functions in the Janowski Domain." Fractal and Fractional 7, no. 6 (2023): 438. http://dx.doi.org/10.3390/fractalfract7060438.

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Many researchers have defined the q-analogous of differential and integral operators for analytic functions using the concept of quantum calculus in the geometric function theory. In this study, we conduct a comprehensive investigation to identify the uses of the Sălăgean q-differential operator for meromorphic multivalent functions. Many features of functions that belong to geometrically defined classes have been extensively studied using differential operators based on q-calculus operator theory. In this research, we extended the idea of the q-analogous of the Sălăgean differential operator for meromorphic multivalent functions using the fundamental ideas of q-calculus. With the help of this operator, we extend the family of Janowski functions by adding two new subclasses of meromorphic q-starlike and meromorphic multivalent q-starlike functions. We discover significant findings for these new classes, including the radius of starlikeness, partial sums, distortion theorems, and coefficient estimates.
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14

Ali, Ekram E., Miguel Vivas-Cortez, and Rabha M. El-Ashwah. "New results about fuzzy $ \mathbf{\gamma } $-convex functions connected with the $ \mathfrak{q} $-analogue multiplier-Noor integral operator." AIMS Mathematics 9, no. 3 (2024): 5451–65. http://dx.doi.org/10.3934/math.2024263.

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<abstract><p>The features of analytical functions were mostly studied using a fuzzy subset and a $ \mathfrak{q} $-difference operator in this study, as we investigate many fuzzy differential subordinations related to the $ \mathfrak{q} $-analogue multiplier-Noor integral operator. By applying fuzzy subordination to univalent functions whose range is symmetric with respect to the real axis, we create a few new subclasses of analytical functions. We define numerous classes related to the family of linear $ \mathfrak{q} $ -operators and introduce them. Here, we focus on the inclusion results and other integral features.</p></abstract>
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15

Kalidolday, A. H., and E. D. Nursultanov. "Interpolation of nonlinear integral Urysohn operators in net spaces." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 105, no. 1 (2022): 66–73. http://dx.doi.org/10.31489/2022m1/66-73.

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In this paper, we study the interpolation properties of the net spaces N_p,q(M), in the case when M is a sufficiently general arbitrary system of measurable subsets from R^n. The integral Urysohn operator is considered. This operator generalizes all linear, integral operators, and non-linear integral operators. The Urysohn operator is not a quasilinear or subadditive operator. Therefore, the classical interpolation theorems for these operators do not hold. A certain analogue of the Marcinkiewicz-type interpolation theorem for this class of operators is obtained. This theorem allows to obtain, in a sense, a strong estimate for Urysohn operators in net spaces from weak estimates for these operators in net spaces with local nets. For example, in order for the Urysohn integral operator in a net space, where the net is the set of all balls in R^n, it is sufficient for it to be of weak type for net spaces, where the net is concentric balls.
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16

Aykol, Canay, and Esra Kaya. "B−maximal operators, B−singular integral operators and B−Riesz potentials in variable exponent Lorentz spaces." Filomat 37, no. 17 (2023): 5765–74. http://dx.doi.org/10.2298/fil2317765a.

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In this paper, we prove the boundedness of B?maximal operator, B?singular integral operator and B?Riesz potential in the variable exponent Lorentz space Lp(?),q(?),?(Rn k,+). As a consequence of the boundedness of B?Riesz potentials in variable exponent Lorentz spaces, we also obtain that B?fractional maximal operators are bounded in Lp(?),q(?),?(Rn k,+).
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17

Abbas, A., F. Fiyaz, S. Mubeen, A. Khan, and T. Abdeljawad. "Some integral inequalities involving q - h fractional integral operator." Journal of Mathematics and Computer Science 38, no. 04 (2025): 535–45. https://doi.org/10.22436/jmcs.038.04.08.

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18

Tariq, Muhammad, Sotiris K. Ntouyas, and Asif Ali Shaikh. "A Comprehensive Review on the Fejér-Type Inequality Pertaining to Fractional Integral Operators." Axioms 12, no. 7 (2023): 719. http://dx.doi.org/10.3390/axioms12070719.

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A review of the results on the fractional Fejér-type inequalities, associated with different families of convexities and different kinds of fractional integrals, is presented. In the numerous families of convexities, it includes classical convex functions, s-convex functions, quasi-convex functions, strongly convex functions, harmonically convex functions, harmonically quasi-convex functions, quasi-geometrically convex functions, p-convex functions, convexity with respect to strictly monotone function, co-ordinated-convex functions, (θ,h−m)−p-convex functions, and h-preinvex functions. Included in the fractional integral operators are Riemann–Liouville fractional integral, (k−p)-Riemann–Liouville, k-Riemann–Liouville fractional integral, Riemann–Liouville fractional integrals with respect to another function, the weighted fractional integrals of a function with respect to another function, fractional integral operators with the exponential kernel, Hadamard fractional integral, Raina fractional integral operator, conformable integrals, non-conformable fractional integral, and Katugampola fractional integral. Finally, Fejér-type fractional integral inequalities for invex functions and (p,q)-calculus are also included.
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19

Palei, Sudhansu, Madan Mohan Soren, Daniel Breaz, and Luminiţa-Ioana Cotîrlǎ. "Sandwich-Type Results and Existence Results of Analytic Functions Associated with the Fractional q-Calculus Operator." Fractal and Fractional 9, no. 1 (2024): 4. https://doi.org/10.3390/fractalfract9010004.

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In the present investigation, we present certain subordination and superordination results for the q-integral operator of a fractional order associated with analytic functions in the open unit disk U. Using this q-integral operator, we obtain sandwich-type results. Furthermore, we employ the existence of univalent solutions to a q-differential equation connected with a fractional q-integral operator of fractional order. We use these results to demonstrate the significance of our findings for particular functions. We also derive some examples and corollaries that are pertinent to our results.
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20

Yang, Heng, and Jiang Zhou. "Some estimates of multilinear operators on tent spaces." Communications in Analysis and Mechanics 16, no. 4 (2024): 700–716. http://dx.doi.org/10.3934/cam.2024031.

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<p>Let $ 0 < \alpha < mn $ and $ 0 < r, q < \infty $. In this paper, we obtain the boundedness of some multilinear operators by establishing pointwise inequalities and applying extrapolation methods on tent spaces $ T_{r}^{q}(\mathbb{R}_{+}^{n+1}) $, where these multilinear operators include multilinear Hardy–Littlewood maximal operator $ \mathcal{M} $, multilinear fractional maximal operator $ \mathcal{M}_{\alpha} $, multilinear Calderón–Zygmund operator $ \mathcal{T} $, and multilinear fractional integral operator $ \mathcal{I}_{\alpha} $. Therefore, the results of Auscher and Prisuelos–Arribas [Math. Z. <bold>286</bold> (2017), 1575–1604] are extended to the general case.</p>
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21

Khan, Qaiser, Muhammad Arif, Mohsan Raza, Gautam Srivastava, Huo Tang, and Shafiq ur Rehman. "Some Applications of a New Integral Operator in q-Analog for Multivalent Functions." Mathematics 7, no. 12 (2019): 1178. http://dx.doi.org/10.3390/math7121178.

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This paper introduces a new integral operator in q-analog for multivalent functions. Using as an application of this operator, we study a novel class of multivalent functions and define them. Furthermore, we present many new properties of these functions. These include distortion bounds, sufficiency criteria, extreme points, radius of both starlikness and convexity, weighted mean and partial sum for this newly defined subclass of multivalent functions are discussed. Various integral operators are obtained by putting particular values to the parameters used in the newly defined operator.
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22

Gopal Bhadana, Krishna, and Ashok Kumar Meena. "ON APPLICATION OF SAIGO’S FRACTIONAL q-INTEGRAL OPERATORS TO BASIC ANALOGUE OF FOX’S H-FUNCTIONS." Jnanabha 52, no. 01 (2022): 118–23. http://dx.doi.org/10.58250/jnanabha.2022.52115.

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This paper deals with the derivation of the Saigo’s fractional q-integral operator of the basic analogue of the Fox’s H-function defined by Saxena, Modi and Kalla [6]. In the present paper, an application of the Saigo’s fractional q-integral operator to various q-integral of Fox’s H-function have been investigated. Some special cases have also been deduced.
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23

Badar, Rizwan Salim. "Applications of $q$-Srivastava-Attiya operator on subclasses of analytic functions." Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74, no. 2 (2025): 254–66. https://doi.org/10.31801/cfsuasmas.1515007.

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The aim of the article is to investigate the applications of $q$-Srivastava-Attiya integral operator on the subclasses of $q$-starlike, $q$-convex and $q$-close-to-convex functions. The results are established by using the subordination result and $q$-analogue of Jack's Lemma. The characteristic properties including necessary condition and its applications, inclusions and integral preservations of the defined classes in the context of $q$-Bernardi operator are established.
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24

Srivastava, H. M., Manish Kumar Bansal, and Priyanka Harjule. "A class of fractional integral operators involving a certain general multiindex Mittag-Leffler function." Ukrains’kyi Matematychnyi Zhurnal 75, no. 8 (2023): 1096–112. http://dx.doi.org/10.3842/umzh.v75i8.863.

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UDC 517.9 This paper is essentially motivated by the demonstrated potential for applications of the presented results in numerous widespread research areas, such as the mathematical, physical, engineering, and statistical sciences. The main object here is to introduce and investigate a class of fractional integral operators involving a certain general family of multiindex Mittag-Leffler functions in their kernel. Among other results obtained in the paper, we establish several interesting expressions for the composition of well-known fractional integral and fractional derivative operators, such as (e.g.) the Riemann–Liouville fractional integral and fractional derivative operators, the Hilfer fractional derivative operator, and the above-mentioned fractional integral operator involving the general family of multiindex Mittag-Leffler functions in its kernel. Our main result is a generalization of the results obtained in earlier investigations on this subject. We also present some potentially useful integral representations for the product of two members of the general family of multiindex Mittag-Leffler functions in terms of the well-known Fox–Wright hypergeometric function p Ψ q with p numerator and q denominator parameters.
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25

Ali, Ekram E., Rabha M. El-Ashwah, Abeer M. Albalahi, and Wael W. Mohammed. "Properties for Close-to-Convex and Quasi-Convex Functions Using q-Linear Operator." Mathematics 13, no. 6 (2025): 900. https://doi.org/10.3390/math13060900.

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In this work, we describe the q-analogue of a multiplier–Ruscheweyh operator of a specific family of linear operators Iq,ρs(ν,τ), and we obtain findings related to geometric function theory (GFT) by utilizing approaches established through subordination and knowledge of q-calculus operators. By using this operator, we develop generalized classes of quasi-convex and close-to-convex functions in this paper. Additionally, the classes Kq,ρs(ν,τ)φ, Qq,ρs(ν,τ)φ are introduced. The invariance of these recently formed classes under the q-Bernardi integral operator is investigated, along with a number of intriguing inclusion relationships between them. Additionally, several unique situations and the beneficial outcomes of these studies are taken into account.
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26

Breaz, Daniel, Abdullah A. Alahmari, Luminiţa-Ioana Cotîrlă, and Shujaat Ali Shah. "On Generalizations of the Close-to-Convex Functions Associated with q-Srivastava–Attiya Operator." Mathematics 11, no. 9 (2023): 2022. http://dx.doi.org/10.3390/math11092022.

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The study of the q-analogue of the classical results of geometric function theory is currently of great interest to scholars. In this article, we define generalized classes of close-to-convex functions and quasi-convex functions with the help of the q-difference operator. Moreover, by using the q-analogues of a certain family of linear operators, the classes Kq,bsh, K˜q,sbh, Qq,bsh, and Q˜q,sbh are introduced. Several interesting inclusion relationships between these newly defined classes are discussed, and the invariance of these classes under the q-Bernadi integral operator was examined. Furthermore, some special cases and useful consequences of these investigations were taken into consideration.
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27

Dumrongpokaphan, Thongchai, Sotiris K. Ntouyas, and Thanin Sitthiwirattham. "Separate Fractional (p,q)-Integrodifference Equations via Nonlocal Fractional (p,q)-Integral Boundary Conditions." Symmetry 13, no. 11 (2021): 2212. http://dx.doi.org/10.3390/sym13112212.

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In this paper, we study a boundary value problem involving (p,q)-integrodifference equations, supplemented with nonlocal fractional (p,q)-integral boundary conditions with respect to asymmetric operators. First, we convert the given nonlinear problem into a fixed-point problem, by considering a linear variant of the problem at hand. Once the fixed-point operator is available, existence and uniqueness results are established using the classical Banach’s and Schaefer’s fixed-point theorems. The application of the main results is demonstrated by presenting numerical examples. Moreover, we study some properties of (p,q)-integral that are used in our study.
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28

Qian, Ruishen. "Embedding Besov type spaces Bp(λ) into tent spaces and Volterra integral operators". Filomat 35, № 15 (2021): 5195–207. http://dx.doi.org/10.2298/fil2115195q.

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In this paper, the boundedness and compactness of embedding from Besov Type spaces Bp(?) into tent spaces Tq,s(?) are investigated (1 ? p ? q < ? and 0 < ?,s < 1). As an application, the boundedness and compactness of Volterra integral operator T1 and integral operator I1 from Besov Type spaces Bp(?) to F(q,q-2+q/p(1-?),s) spaces are also studied.
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29

Elhaddad, Suhila, Huda Aldweby, and Maslina Darus. "Univalence of New General Integral Operator Defined by the Ruscheweyh Type q-Difference Operator." European Journal of Pure and Applied Mathematics 13, no. 4 (2020): 861–72. http://dx.doi.org/10.29020/nybg.ejpam.v13i4.3817.

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In this study , by employing the Ruscheweyh type q-analogue operator we consider a new family of integral operators on the space of analytical functions. For this family, we demonstrate some sufficient conditions of univalence criteria on the class of analytical functions.
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30

Al-shbeil, Isra, Shahid Khan, Hala AlAqad, Salam Alnabulsi, and Mohammad Faisal Khan. "Applications of the Symmetric Quantum-Difference Operator for New Subclasses of Meromorphic Functions." Symmetry 15, no. 7 (2023): 1439. http://dx.doi.org/10.3390/sym15071439.

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Our goal in this article is to use ideas from symmetric q-calculus operator theory in the study of meromorphic functions on the punctured unit disc and to propose a novel symmetric q-difference operator for these functions. A few additional classes of meromorphic functions are then defined in light of this new symmetric q-difference operator. We prove many useful conclusions regarding these newly constructed classes of meromorphic functions, such as convolution, subordination features, integral representations, and necessary conditions. The technique presented in this article may be used to produce a wide variety of new types of generalized symmetric q-difference operators, which can subsequently be used to investigate a wide variety of new classes of analytic and meromorphic functions related to symmetric quantum calculus.
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31

Jayprakash, Yadav. "Certain q-Kober fractional integral operator of generalized basic hypergeometric functions and q-polynomials." International Journal of Mathematics and Computer Research 13, no. 04 (2025): 5114–25. https://doi.org/10.5281/zenodo.15268505.

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The object of this paper is to established the Kober fractional integral operator of the generalized basic hypergeometric function.Interestingly Kober fractional integral operator of various q-polynomials have been expressed in terms of the basic  analogue of Kamp˙e de F˙eriet function.Some special cases have been deduced as an application of main result.
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32

Noor, Khalida Inayat, and Shujaat Ali Shah. "Study of the Q-spiral-like functions of complex order." Mathematica Slovaca 71, no. 1 (2021): 75–82. http://dx.doi.org/10.1515/ms-2017-0453.

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Abstract This paper aims to introduce the q-analogue of subclasses of the spiral-like functions of complex order and derive some inclusion properties by applying certain linear operators. The invariance of these classes under q-Bernardi integral operator has been discussed. Our results yield some known results as special case.
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33

Khan, Mohammad Faisal, and Mohammed AbaOud. "New Applications of Fractional q-Calculus Operator for a New Subclass of q-Starlike Functions Related with the Cardioid Domain." Fractal and Fractional 8, no. 1 (2024): 71. http://dx.doi.org/10.3390/fractalfract8010071.

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Recently, a number of researchers from different fields have taken a keen interest in the domain of fractional q-calculus on the basis of fractional integrals and derivative operators. This has been used in various scientific research and technology fields, including optics, mathematical biology, plasma physics, electromagnetic theory, and many more. This article explores some mathematical applications of the fractional q-differential and integral operator in the field of geometric function theory. By using the linear multiplier fractional q-differintegral operator Dq,λmρ,σ and subordination, we define and develop a collection of q-starlike functions that are linked to the cardioid domain. This study also investigates sharp inequality problems like initial coefficient bounds, the Fekete–Szego problems, and the coefficient inequalities for a new class of q-starlike functions in the open unit disc U. Furthermore, we analyze novel findings with respect to the inverse function (μ−1) within the class of q-starlike functions in U. The findings in this paper are easy to understand and show a connection between present and past studies.
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34

Faraj, Ahmad, Tariq Salim, Safaa Sadek, and Jamal Ismail. "Generalized Mittag-Leffler Function Associated with Weyl Fractional Calculus Operators." Journal of Mathematics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/821762.

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This paper is devoted to study further properties of generalized Mittag-Leffler functionEα,β,pγ,δ,qassociated with Weyl fractional integral and differential operators. A new integral operatorℰα,β,p,w,∞γ,δ,qdepending on Weyl fractional integral operator and containingEα,β,pγ,δ,q(z)in its kernel is defined and studied, namely, its boundedness. Also, composition of Weyl fractional integral and differential operators with the new operatorℰα,β,p,w,∞γ,δ,qis established.
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35

Palei, Sudhansu, Madan Mohan Soren, and Luminiţa-Ioana Cotîrlǎ. "Coefficient Bounds for Alpha-Convex Functions Involving the Linear q-Derivative Operator Connected with the Cardioid Domain." Fractal and Fractional 9, no. 3 (2025): 172. https://doi.org/10.3390/fractalfract9030172.

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Scholars from several disciplines have recently expressed interest in the field of fractional q-calculus based on fractional integrals and derivative operators. This article mathematically applies the fractional q-differential and q-integral operators in geometric function theory. The linear q-derivative operator Sμ,δ,qn,m and subordination are used in this study to define and construct new classes of α-convex functions associated with the cardioid domain. Additionally, this paper explores acute inequality problems for newly defined classes Rqα(a,c,m,L,P), of α-convex functions in the open unit disc Us, such as initial coefficient bounds, coefficient inequalities, Fekete–Szegö problems, the second Hankel determinants, and logarithmic coefficients. The results presented in this paper are simple to comprehend and demonstrate how current research relates to earlier research. We found all of the estimates, and they are sharp.
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36

Ernst, Thomas. "On Various Formulas with q-integralsand Their Applications to q-hypergeometric Functions." European Journal of Pure and Applied Mathematics 13, no. 5 (2020): 1241–59. http://dx.doi.org/10.29020/nybg.ejpam.v13i5.3755.

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We present three q-Taylor formulas with q-integral remainder. The two last proofsrequire a slight rearrangement by a well-known formula. The first formula has been given in different form by Annaby and Mansour. We give concise proofs for q-analogues of Eulerian integral formulas for general q-hypergeometric functions corresponding to Erd ́elyi, and for two of Srivastavas triple hypergeometric functions and other functions. All proofs are made in a similar style by using q-integration. We find some new formulas for fractional q-integrals including a series expansion. In the same way, the operator formulas by Srivastava and Manocha find a natural generalization.
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37

Khan, Mohammad Faisal, Isra Al-shbeil, Shahid Khan, Nazar Khan, Wasim Ul Haq, and Jianhua Gong. "Applications of a q-Differential Operator to a Class of Harmonic Mappings Defined by q-Mittag–Leffler Functions." Symmetry 14, no. 9 (2022): 1905. http://dx.doi.org/10.3390/sym14091905.

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Many diverse subclasses of analytic functions, q-starlike functions, and symmetric q-starlike functions have been studied and analyzed by using q-analogous values of integral and derivative operators. In this paper, we define a q-analogous value of differential operators for harmonic functions with the help of basic concepts of quantum (q-) calculus operator theory; and introduce a new subclass of harmonic functions associated with the Janowski and q-Mittag–Leffler functions. We obtain several useful properties of the new class, such as necessary and sufficient conditions, criteria for analyticity, compactness, convexity, extreme points, radii of starlikeness, radii of convexity, distortion bounds, and integral mean inequality. Furthermore, we discuss some applications of this study in the form of some results and examples and highlight some known corollaries for verifying our main results presented in this investigation. Finally, the conclusion section summarizes the fact about the (p,q)-variations.
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38

Al-Shbeil, Isra, Hari Mohan Srivastava, Muhammad Arif, Mirajul Haq, Nazar Khan, and Bilal Khan. "Majorization Results Based upon the Bernardi Integral Operator." Symmetry 14, no. 7 (2022): 1404. http://dx.doi.org/10.3390/sym14071404.

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By making use of some families of integral and derivative operators, many distinct subclasses of analytic, starlike functions, and symmetric starlike functions have already been defined and investigated from numerous perspectives. In this article, with the help of the one-parameter Bernardi integral operator, we investigate several majorization results for the class of normalized starlike functions, which are associated with the Janowski functions. We also give some particular cases of our main results. Finally, we direct the interested readers to the possibility of examining the fundamental or quantum (or q-) extensions of the findings provided in this work in the concluding section. However, the (p,q)-variations of the suggested q-results will provide relatively minor and inconsequential developments because the additional (rather forced-in) parameter p is obviously redundant.
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39

Mahmood, Shahid, Nusrat Raza, Eman S. A. AbuJarad, Gautam Srivastava, H. M. Srivastava, and Sarfraz Nawaz Malik. "Geometric Properties of Certain Classes of Analytic Functions Associated with a q-Integral Operator." Symmetry 11, no. 5 (2019): 719. http://dx.doi.org/10.3390/sym11050719.

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This article presents certain families of analytic functions regarding q-starlikeness and q-convexity of complex order γ ( γ ∈ C \ 0 ) . This introduced a q-integral operator and certain subclasses of the newly introduced classes are defined by using this q-integral operator. Coefficient bounds for these subclasses are obtained. Furthermore, the ( δ , q )-neighborhood of analytic functions are introduced and the inclusion relations between the ( δ , q )-neighborhood and these subclasses of analytic functions are established. Moreover, the generalized hyper-Bessel function is defined, and application of main results are discussed.
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40

Najafzadeh, Shahram, and Mugur Acu. "q–analogue of generalized Ruschweyh operator related to a new subfamily of multivalent functions." General Mathematics 27, no. 2 (2019): 59–69. http://dx.doi.org/10.2478/gm-2019-0015.

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AbstractA new subfamily of p–valent analytic functions with negative coefficients in terms of q–analogue of generalized Ruschweyh operator is considered. Several properties concerning coefficient bounds, weighted and arithmetic mean, radii of starlikeness, convexity and close-to-convexity are obtained. A family of class preserving integral operators and integral representation are also indicated.
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41

Kokilashvili, Vakhtang, Mieczysław Mastyło, and Alexander Meskhi. "Compactness criteria for fractional integral operators." Fractional Calculus and Applied Analysis 22, no. 5 (2019): 1269–83. http://dx.doi.org/10.1515/fca-2019-0067.

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Abstract We establish necessary and sufficient conditions for the compactness of fractional integral operators from Lp(X, μ) to Lq(X, μ) with 1 < p < q < ∞, where μ is a measure on a quasi-metric measure space X. As an application we obtain criteria for the compactness of fractional integral operators defined in weighted Lebesgue spaces over bounded domains of the Euclidean space ℝn with the Lebesgue measure, and also for the fractional integral operator associated to rectifiable curves of the complex plane.
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42

Guliyev, Vagif S., and Yagub Y. Mammadov. "Riesz potential on the Heisenberg group and modified Morrey spaces." Analele Universitatii "Ovidius" Constanta - Seria Matematica 20, no. 1 (2012): 189–212. http://dx.doi.org/10.2478/v10309-012-0013-8.

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Abstract In this paper we study the fractional maximal operator Mα, 0 ≤ α < Q and the Riesz potential operator ℑα, 0 < α < Q on the Heisenberg group in the modified Morrey spaces L͂p,λ(ℍn), where Q = 2n + 2 is the homogeneous dimension on ℍn. We prove that the operators Mα and ℑα are bounded from the modified Morrey space L͂1,λ(ℍn) to the weak modified Morrey space WL͂q,λ(ℍn) if and only if, α/Q ≤ 1 - 1/q ≤ α/(Q - λ) and from L͂p,λ(ℍn) to L͂q,λ(ℍn) if and only if, α/Q ≤ 1/p - 1/q ≤ α/(Q - λ).In the limiting case we prove that the operator Mα is bounded from L͂p,λ(ℍn) to L∞(ℍn) and the modified fractional integral operator Ĩα is bounded from L͂p,λ(ℍn) to BMO(ℍn).As applications of the properties of the fundamental solution of sub-Laplacian Ը on ℍn, we prove two Sobolev-Stein embedding theorems on modified Morrey and Besov-modified Morrey spaces in the Heisenberg group setting. As an another application, we prove the boundedness of ℑα from the Besov-modified Morrey spaces BL͂spθ,λ(ℍn) to BL͂spθ,λ(ℍn).
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43

Badar, Rizwan Salim, and Khalida Inayat Noor. "q-Generalized Linear Operator on Bounded Functions of Complex Order." Mathematics 8, no. 7 (2020): 1149. http://dx.doi.org/10.3390/math8071149.

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This article presents a q-generalized linear operator in Geometric Function Theory (GFT) and investigates its application to classes of analytic bounded functions of complex order S q ( c ; M ) and C q ( c ; M ) where 0 < q < 1 , 0 ≠ c ∈ C , and M > 1 2 . Integral inclusion of the classes related to the q-Bernardi operator is also proven.
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44

Xi, Gao-Wen, and Qiu-Ming Luo. "A Further Extension for Ramanujan’s Beta Integral and Applications." Mathematics 7, no. 2 (2019): 118. http://dx.doi.org/10.3390/math7020118.

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In 1915, Ramanujan stated the following formula ∫ 0 ∞ t x - 1 ( - a t ; q ) ∞ ( - t ; q ) ∞ d t = π sin π x ( q 1 - x , a ; q ) ∞ ( q , a q - x ; q ) ∞ , where 0 < q < 1 , x > 0 , and 0 < a < q x . The above formula is called Ramanujan’s beta integral. In this paper, by using q-exponential operator, we further extend Ramanujan’s beta integral. As some applications, we obtain some new integral formulas of Ramanujan and also show some new representation with gamma functions and q-gamma functions.
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45

Hadi, Sarem H., Maslina Darus, Firas Ghanim, and Alina Alb Lupaş. "Sandwich-Type Theorems for a Family of Non-Bazilevič Functions Involving a q-Analog Integral Operator." Mathematics 11, no. 11 (2023): 2479. http://dx.doi.org/10.3390/math11112479.

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This article presents a new q-analog integral operator, which generalizes the q-Srivastava–Attiya operator. Using this q-analog operator, we define a family of analytic non-Bazilevič functions, denoted as Tq,τ+1,uμ(ϑ,λ,M,N). Furthermore, we investigate the differential subordination properties of univalent functions using q-calculus, which includes the best dominance, best subordination, and sandwich-type properties. Our results are proven using specialized techniques in differential subordination theory.
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46

Munir, Arslan, Hüseyin Budak, Irza Faiz та Shahid Qaisar. "Generalizations of Simpson type inequality for (α,m)-convex functions". Filomat 38, № 10 (2024): 3295–312. https://doi.org/10.2298/fil2410295m.

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Several scholars are interested in fractional operators with integral inequalities. Due to its characteristics and wide range of applications in science, engineering fields, artificial intelligence and frac-tional inequalities should be employed in mathematical investigations. In this paper, we establish the new identity for the Caputo-Fabrizio fractional integral operator. By utilizing this identity, the generalization of Si mpsonty pein equalityfo r(? ,m )-convex functions via the Caputo-Fabrizio fractional integral operator. Furthermore, we also include the applications to special means, q-digamma functions, Simpson formula, Matrix inequalities, Modified Bessel function, and mind-point formula. These applications have given a new dimension to scholars.
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47

Azzam, Abdel Fatah, Shujaat Ali Shah, Alhanouf Alburaikan та Sheza M. El-Deeb. "Certain Inclusion Properties for the Class of q-Analogue of Fuzzy α-Convex Functions". Symmetry 15, № 2 (2023): 509. http://dx.doi.org/10.3390/sym15020509.

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Recently, the properties of analytic functions have been mainly discussed by means of a fuzzy subset and a q-difference operator. We define certain new subclasses of analytic functions by using the fuzzy subordination to univalent functions whose range is symmetric with respect to the real axis. We introduce the family of linear q-operators and define various classes associated with these operators. The inclusion results and various integral properties are the main investigations of this article.
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48

Khan, Mohammad Faisal, Anjali Goswami, and Shahid Khan. "Certain New Subclass of Multivalent Q-Starlike Functions Associated with Q-Symmetric Calculus." Fractal and Fractional 6, no. 7 (2022): 367. http://dx.doi.org/10.3390/fractalfract6070367.

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In our present investigation, we extend the idea of q-symmetric derivative operators to multivalent functions and then define a new subclass of multivalent q-starlike functions. For this newly defined function class, we discuss some useful properties of multivalent functions, such as the Hankel determinant, symmetric Toeplitz matrices, the Fekete–Szego problem, and upper bounds of the functional ap+1−μap+12 and investigate some new lemmas for our main results. In addition, we consider the q-Bernardi integral operator along with q-symmetric calculus and discuss some applications of our main results.
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49

Akbulut, Ali, and Amil Hasanov. "Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces." Open Mathematics 14, no. 1 (2016): 1023–38. http://dx.doi.org/10.1515/math-2016-0090.

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AbstractIn this paper, we study the boundedness of fractional multilinear integral operators with rough kernels $T_{\Omega ,\alpha }^{{A_1},{A_2}, \ldots ,{A_k}},$ which is a generalization of the higher-order commutator of the rough fractional integral on the generalized weighted Morrey spaces Mp,ϕ (w). We find the sufficient conditions on the pair (ϕ1, ϕ2) with w ∈ Ap,q which ensures the boundedness of the operators $T_{\Omega ,\alpha }^{{A_1},{A_2}, \ldots ,{A_k}},$ from ${M_{p,{\varphi _1}}}\left( {{w^p}} \right)\,{\rm{to}}\,{M_{p,{\varphi _2}}}\left( {{w^q}} \right)$ for 1 < p < q < ∞. In all cases the conditions for the boundedness of the operator $T_{\Omega ,\alpha }^{{A_1},{A_2}, \ldots ,{A_k}},$ are given in terms of Zygmund-type integral inequalities on (ϕ1, ϕ2) and w, which do not assume any assumption on monotonicity of ϕ1 (x,r), ϕ2(x, r) in r.
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50

Ali, Ekram E., Rabha M. El-Ashwah, Abeer M. Albalahi, R. Sidaoui, and Abdelkader Moumen. "Inclusion properties for analytic functions of $ q $-analogue multiplier-Ruscheweyh operator." AIMS Mathematics 9, no. 3 (2024): 6772–83. http://dx.doi.org/10.3934/math.2024330.

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<abstract><p>The results of this work have a connection with the geometric function theory and they were obtained using methods based on subordination along with information on $ \mathfrak{q} $-calculus operators. We defined the $ \mathfrak{q} $-analogue of multiplier- Ruscheweyh operator of a certain family of linear operators $ I_{\mathfrak{q}, \mu }^{s}(\lambda, \ell) \mathfrak{f}(\varsigma) \; (s\in \mathbb{N}_{0} = \mathbb{N}\cup \{0\}, \mathbb{ N} = \left\{ 1, 2, 3, ..\right\}; \ell, \lambda, \mu \geq 0, 0 < \mathfrak{q} < 1) $. Our major goal was to build some analytic function subclasses using $ I_{ \mathfrak{q}, \mu }^{s}(\lambda, \ell)\mathfrak{f}(\varsigma) $ and to look into various inclusion relationships that have integral preservation features.</p></abstract>
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