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Journal articles on the topic 'Integral Operator'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 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 Hadama

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2

Ayryan, E. A., M. Hnatic, and V. B. Malyutin. "On the equivalence of operator and combinatorial approaches for onestep random Markov processes." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 58, no. 1 (2022): 21–33. http://dx.doi.org/10.29235/1561-2430-2022-58-1-21-33.

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Herein, for one-step random Markov processes the comparison of the operator and combinatorial methods based on the use of functional integrals is performed. With the combinatorial approach, the transition from the stochastic differential equation to the functional integral is used. This allows us to obtain the expression for the mean population size in terms of the functional integral. With the operator approach, the transition to the functional integral is performed via the creation and annihilation operators. It is shown that the mean values calculated using the functional integrals arising

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3

Luo, Min-Jie, and Ravinder Krishna Raina. "On the Composition Structures of Certain Fractional Integral Operators." Symmetry 14, no. 9 (2022): 1845. http://dx.doi.org/10.3390/sym14091845.

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This paper investigates the composition structures of certain fractional integral operators whose kernels are certain types of generalized hypergeometric functions. It is shown how composition formulas of these operators can be closely related to the various Erdélyi-type hypergeometric integrals. We also derive a derivative formula for the fractional integral operator and some applications of the operator are considered for a certain Volterra-type integral equation, which provide two generalizations to Khudozhnikov’s integral equation (see below). Some specific relationships, examples, and som

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4

Zhang, Zhiqiang, Ghulam Farid, Sajid Mehmood, Kamsing Nonlaopon, and Tao Yan. "Generalized k-Fractional Integral Operators Associated with Pólya-Szegö and Chebyshev Types Inequalities." Fractal and Fractional 6, no. 2 (2022): 90. http://dx.doi.org/10.3390/fractalfract6020090.

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Inequalities related to derivatives and integrals are generalized and extended via fractional order integral and derivative operators. The present paper aims to define an operator containing Mittag-Leffler function in its kernel that leads to deduce many already existing well-known operators. By using this generalized operator, some well-known inequalities are studied. The results of this paper reproduce Chebyshev and Pólya-Szegö type inequalities for Riemann-Liouville and many other fractional integral operators.

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Lupaş, Alina Alb, and Loriana Andrei. "Certain Integral Operators of Analytic Functions." Mathematics 9, no. 20 (2021): 2586. http://dx.doi.org/10.3390/math9202586.

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In this paper, two new integral operators are defined using the operator DRλm,n, introduced and studied in previously published papers, defined by the convolution product of the generalized Sălăgean operator and Ruscheweyh operator. The newly defined operators are used for introducing several new classes of functions, and properties of the integral operators on these classes are investigated. Subordination results for the differential operator DRλm,n are also obtained.

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6

Harjule, Priyanka, Manish Bansal, and Serkan Araci. "An investigation of incomplete H−functions associated with some fractional integral operators." Filomat 36, no. 8 (2022): 2695–703. http://dx.doi.org/10.2298/fil2208695h.

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Arbitrary-order integral operators find variety of implementations in different science disciplines as well as engineering fields. The study presented as part of this research paper derives motivation from the fact that applications of fractional operators and special functions demonstrate a huge potential in understanding many of physical phenomena. Study and investigation of a fractional integral operator containing an incomplete H? functions (IHFs) as the kernel is the primary objective of the research work presented here. Specifically, few interesting relations involving the new fractional

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7

Paul, Supriya Kumar, Lakshmi Narayan Mishra, and Vishnu Narayan Mishra. "Results on integral inequalities for a generalized fractional integral operator unifying two existing fractional integral operators." Nonlinear Analysis: Modelling and Control 29, no. 6 (2024): 1080–105. https://doi.org/10.15388/namc.2024.29.37848.

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The main aim of this article is to design a novel framework to study a generalized fractional integral operator that unifies two existing fractional integral operators. To ensure the suitable selection of the operator and with the discussion of special cases, it is shown that our considered fractional integral generalizes the well-known Atangana–Baleanu fractional integral (AB-fractional integral) and the ABK-fractional integral. Conditions are stated for the generalized AB-fractional integral operator (GAB-fractional integral operator) to be bounded in the space Xcp (γ1,γ2). We also provide a

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8

Lanzhe, Liu. "Continuity for some multilinear operators of integral operators on Triebel-Lizorkin spaces." International Journal of Mathematics and Mathematical Sciences 2004, no. 38 (2004): 2039–47. http://dx.doi.org/10.1155/s0161171204303121.

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The continuityfor some multilinear operators related to certain fractional singular integral operators on Triebel-Lizorkin spaces is obtained. The operators include Calderon-Zygmund singular integral operator and fractional integral operator.

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9

Liu, Lanzhe. "Estimates of multilinear singular integral operators and mean oscillation." Publications de l'Institut Math?matique (Belgrade) 95, no. 109 (2014): 201–14. http://dx.doi.org/10.2298/pim1409201l.

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We prove the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue spaces to Orlicz spaces. The operators include Calder?n-Zygmund singular integral operator, Littlewood-Paley operator and Marcinkiewicz operator.

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10

Rahman, Gauhar, Zafar Ullah, Aftab Khan, Erhan Set, and Kottakkaran Sooppy Nisar. "Certain Chebyshev-Type Inequalities Involving Fractional Conformable Integral Operators." Mathematics 7, no. 4 (2019): 364. http://dx.doi.org/10.3390/math7040364.

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Since an interesting functional by P.L. Chebyshev was presented in the year 1882, many results, which are called Chebyshev-type inequalities, have been established. Some of these inequalities were obtained by using fractional integral operators. Very recently, a new variant of the fractional conformable integral operator was introduced by Jarad et al. Motivated by this operator, we aim at establishing novel inequalities for a class of differentiable functions, which are associated with Chebyshev’s functional, by employing a fractional conformable integral operator. We also aim at showing impor

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11

Girardi, Maria, and Lutz Weis. "Integral operators with operator-valued kernels." Journal of Mathematical Analysis and Applications 290, no. 1 (2004): 190–212. http://dx.doi.org/10.1016/j.jmaa.2003.09.044.

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12

Hasanov, J. J., I. Ekincioglu, and C. Keskin. "A characterization for $B$-singular integral operator and its commutators on generalized weighted $B$-Morrey spaces." Carpathian Mathematical Publications 15, no. 1 (2023): 196–211. http://dx.doi.org/10.15330/cmp.15.1.196-211.

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We study the maximal operator $M_{\gamma}$ and the singular integral operator $A_{\gamma}$, associated with the generalized shift operator. The generalized shift operators are associated with the Laplace-Bessel differential operator. Our analysis is based on two weighted inequalities for the maximal operator, singular integral operators, and their commutators, related to the Laplace-Bessel differential operator in generalized weighted $B$-Morrey spaces.

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13

Bouzeffour, Fethi. "Fractional Integrals Associated with the One-Dimensional Dunkl Operator in Generalized Lizorkin Space." Symmetry 15, no. 9 (2023): 1725. http://dx.doi.org/10.3390/sym15091725.

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This paper explores the realm of fractional integral calculus in connection with the one-dimensional Dunkl operator on the space of tempered functions and Lizorkin type space. The primary objective is to construct fractional integral operators within this framework. By establishing the analogous counterparts of well-known operators, including the Riesz fractional integral, Feller fractional integral, and Riemann–Liouville fractional integral operators, we demonstrate their applicability in this setting. Moreover, we show that familiar properties of fractional integrals can be derived from the

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14

Breaz, Nicoleta. "Properties of Univalence for a New General Integral Operator Defined as a Joint Extension of Two Known Integral Operators." Journal of Function Spaces 2023 (March 27, 2023): 1–5. http://dx.doi.org/10.1155/2023/8183191.

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In this paper, we consider a new general integral operator, defined as a joint extension of two already known integral operators, and prove some univalence properties for this operator. Some other well-known operators are mentioned as particular cases of our general operator, and known results are outlined also as particular cases of our results.

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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,

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16

Zayed, Mohra, and Ahmed Bakhet. "Some Results of R-Matrix Functions and Their Fractional Calculus." Fractal and Fractional 9, no. 2 (2025): 82. https://doi.org/10.3390/fractalfract9020082.

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In this study, we explore various fractional integral properties of R-matrix functions using the Hilfer fractional derivative operator within the framework of fractional calculus. We introduce the θ integral operator and extend its definition to include the R matrix functions. The composition of Riemann–Liouville fractional integral and differential operators is determined using the θ-integral operator. Additionally, we investigate the compositional properties of θ-integral operators, and we establish their inversion, offering new insights into their structural and functional characteristics.

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17

Hu, Yi, Ghulam Farid, Zijiang, and Kahkashan Mahreen. "Bounds of a Unified Integral Operator via Exponentially s,m-Convexity and Their Consequences." Journal of Function Spaces 2020 (May 22, 2020): 1–10. http://dx.doi.org/10.1155/2020/3530591.

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Various known fractional and conformable integral operators can be obtained from a unified integral operator. The aim of this paper is to find bounds of this unified integral operator via exponentially s,m-convex functions. The resulting bounds provide compact formulas for the bounds of associated fractional and conformable integral operators. Several Hadamard-type inequalities have been produced from a compact version for unified integral operators for exponentially s,m-convex functions.

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18

Yonghui, Cao, and Zhou Jiang. "Morrey Spaces for Nonhomogeneous Metric Measure Spaces." Abstract and Applied Analysis 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/196459.

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The authors give a definition of Morrey spaces for nonhomogeneous metric measure spaces and investigate the boundedness of some classical operators including maximal operator, fractional integral operator, and Marcinkiewicz integral operators.

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19

Liu, Lanzhe. "Weighted boundedness for Toeplitz type operator associated to general integral operators." Asian-European Journal of Mathematics 07, no. 02 (2014): 1450026. http://dx.doi.org/10.1142/s1793557114500260.

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In this paper, we establish the weighted sharp maximal function estimates for the Toeplitz type operators associated to some integral operators and the weighted Lipschitz and BMO functions. As an application, we obtain the boundedness of the Toeplitz type operators on weighted Lebesgue and Morrey spaces. The operator includes Littlewood–Paley operator, Marcinkiewicz operator and Bochner–Riesz operator.

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20

Potseiko, Pavel Gennadjevich, and Evgeny Alekseevich Rovba. "Approximations of one singular integral on an interval by Fourier-Chebyshev rational integral operators." Sbornik: Mathematics 215, no. 7 (2024): 953–92. http://dx.doi.org/10.4213/sm10030e.

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We study approximations on the interval $[-1,1]$ of singular integrals of the form $$ \widehat{f}(x)=\int_{-1}^{1}\frac{f(t)}{t-x}\sqrt{1-t^2} dt, \qquad x \in [-1,1], $$ by two rational integral operators related to each other in a certain sense. The first is the Fourier-Chebyshev integral operator associated with the Chebyshev-Markov system of rational functions. The second operator is its image under the transformation by the singular integral under consideration. Approximative properties of the corresponding polynomial analogues of both operators are studied in the case where the density o

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21

Xia, Xiuyun, Huatao Chen, Hao Tian, Ye Wang, and Yadan Shi. "Sharp and Weighted Boundedness for Multilinear Integral Operators." Tatra Mountains Mathematical Publications 86, no. 1 (2024): 185–204. http://dx.doi.org/10.2478/tmmp-2024-0017.

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Abstract In this paper, the weighted boundedness for some multilinear operators related to the Littlewood-Paley operator and Marcinkiewicz operator on the generalized Morrey spaces are obtained by using the sharp estimates of the multilinear operators.

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22

Azizah, Siti Rohmah, Hairur Rahman, and Achmad Nasichuddin. "Ketaksamaan Operator Integral Fraksional yang Diperumum pada Ruang Morrey Tak Homogen yang Diperumum." Jurnal Riset Mahasiswa Matematika 3, no. 5 (2024): 251–57. http://dx.doi.org/10.18860/jrmm.v3i5.16970.

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A Fractional integral operator is one of the operators in mathematical analysis. Fractional integral operator itself maps any real-valued function into the integral form of the division of the at function. One of the expansion of fractional integral operator is generalized fractional integral operator. Morrey space is an extension of Lebesgue space. Morrey space is the set of all Lebesgue measurable functions, whose norm is finite over Morrey space. In this study, we will discuss the inequalities of the generalized fractional integral operator on a generalized non-homogeneous Morrey space. We

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23

Shahmurov, Rishad. "On Integral Operators with Operator-Valued Kernels." Journal of Inequalities and Applications 2010, no. 1 (2010): 850125. http://dx.doi.org/10.1155/2010/850125.

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24

Lasode, Ayotunde Olajide, Timothy Oloyede Opoola, Isra Al-Shbeil, Timilehin Gideon Shaba, and Huda Alsaud. "Concerning a Novel Integral Operator and a Specific Category of Starlike Functions." Mathematics 11, no. 21 (2023): 4519. http://dx.doi.org/10.3390/math11214519.

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In this study, a novel integral operator that extends the functionality of some existing integral operators is presented. Specifically, the integral operator acts as the inverse operator to the widely recognized Opoola differential operator. By making use of the integral operator, a certain subclass of analytic univalent functions defined in the unit disk is proposed and investigated. This new class encompasses some familiar subclasses, like the class of starlike and the class of convex functions, while some new ones are introduced. The investigation thereafter covers coefficient inequality, d

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25

Yuan, Hongfen, Guohong Shi, and Xiushen Hu. "Boundary Value Problems for the Perturbed Dirac Equation." Axioms 13, no. 4 (2024): 238. http://dx.doi.org/10.3390/axioms13040238.

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The perturbed Dirac operators yield a factorization for the well-known Helmholtz equation. In this paper, using the fundamental solution for the perturbed Dirac operator, we define Cauchy-type integral operators (singular integral operators with a Cauchy kernel). With the help of these operators, we investigate generalized Riemann and Dirichlet problems for the perturbed Dirac equation which is a higher-dimensional generalization of a Vekua-type equation. Furthermore, applying the generalized Cauchy-type integral operator F˜λ, we construct the Mann iterative sequence and prove that the iterati

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26

Hovhannisyan, A. H., A. H. Kamalyan, and H. A. Kamalyan. "ON A CONNECTION BETWEEN A CLASS OF SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS AND INTEGRAL OPERATORS WITH SEMI-SEPARABLE KERNEL." Proceedings of the YSU A: Physical and Mathematical Sciences 52, no. 2 (246) (2018): 77–83. http://dx.doi.org/10.46991/pysu:a/2018.52.2.077.

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In the present paper the connection between a class of systems of differential equations and integral operators with semi-separable kernel is established. Using a matrix of the system the inverse to a given integral operator is constructed. Moreover by putting some additional conditions on the kernel of integral operator and by the help of inverse of integral operator a fundamental matrix of the system is constructed.

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27

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. Include

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28

Labrigui, Hatim, Mohamed Rossafi, Abdeslam Touri, and Samir Kabbaj. "Integral K-operator frames for B(H)." Annals of the University of Craiova - Mathematics and Computer Science Series 48, no. 1 (2021): 244–57. http://dx.doi.org/10.52846/ami.v48i1.1385.

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In this paper, we will introduce a new notion, that of $K$-Integral operator frames in the set of all bounded linear operators noted $\mathcal{B}(H)$, where $H$ is a separable Hilbert space. Also, we prove some results of integral $K$-operator frame. Lastly we will establish some new properties for the perturbation and stability for an integral $K$-operator frames for $\mathcal{B}(H)$.

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29

Al-Omari, Shrideh Khalaf. "On some variant of a whittaker integral operator and its representative in a class of square integrable Boehmians." Boletim da Sociedade Paranaense de Matemática 38, no. 1 (2018): 173. http://dx.doi.org/10.5269/bspm.v38i1.36468.

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This paper investigates some variant of Whittaker integral operators on a class of square integrable Boehmians. We define convolution products and derive the convolution theorem which substantially satisfy the axioms necessary for generating the Whittaker spaces of Boehmians. Relied on this analysis, we give a definition and properties of the Whittaker integral operator in the class of square integrable Boehmians. The extended Whittaker integral operator, is well-defined, linear and coincides with the classical integral in certain properties.

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30

Gunawan, Hendra, Denny Ivanal Hakim, Yoshihiro Sawano, and Idha Sihwaningrum. "Weak Type Inequalities for Some Integral Operators on Generalized Nonhomogeneous Morrey Spaces." Journal of Function Spaces and Applications 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/809704.

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We prove weak type inequalities for some integral operators, especially generalized fractional integral operators, on generalized Morrey spaces of nonhomogeneous type. The inequality for generalized fractional integral operators is proved by using two different techniques: one uses the Chebyshev inequality and some inequalities involving the modified Hardy-Littlewood maximal operator and the other uses a Hedberg type inequality and weak type inequalities for the modified Hardy-Littlewood maximal operator. Our results generalize the weak type inequalities for fractional integral operators on ge

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31

Oros, Georgia Irina, Gheorghe Oros, and Shigeyoshi Owa. "Subordination Properties of Certain Operators Concerning Fractional Integral and Libera Integral Operator." Fractal and Fractional 7, no. 1 (2022): 42. http://dx.doi.org/10.3390/fractalfract7010042.

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The results contained in this paper are the result of a study regarding fractional calculus combined with the classical theory of differential subordination established for analytic complex valued functions. A new operator is introduced by applying the Libera integral operator and fractional integral of order λ for analytic functions. Many subordination properties are obtained for this newly defined operator by using famous lemmas proved by important scientists concerned with geometric function theory, such as Eenigenburg, Hallenbeck, Miller, Mocanu, Nunokawa, Reade, Ruscheweyh and Suffridge.

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32

Schep, Anton R. "Compactness Properties of Carleman and Hille-Tamarkin Operators." Canadian Journal of Mathematics 37, no. 5 (1985): 921–33. http://dx.doi.org/10.4153/cjm-1985-050-3.

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In this paper we study integral operators with domain a Banach function space Lρ1 and range another Banach function space Lρ2 or the space L0 of all measurable functions. Recall that a linear operator T from Lρ1 into L0 is called an integral operator if there exists a μ × v-measurable function T(x, y) on X × Y such thatSuch an integral operator is called a Carleman integral operator if for almost every x ∊ X the functionis an element of the associate space L′ρ1, i.e.,

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33

FRANZ, UWE, RÉMI LÉANDRE, and RENÉ SCHOTT. "MALLIAVIN CALCULUS AND SKOROHOD INTEGRATION FOR QUANTUM STOCHASTIC PROCESSES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 04, no. 01 (2001): 11–38. http://dx.doi.org/10.1142/s0219025701000371.

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A derivation operator and a divergence operator are defined on the algebra of bounded operators on the symmetric Fock space over the complexification of a real Hilbert space [Formula: see text] and it is shown that they satisfy similar properties as the derivation and divergence operator on the Wiener space over [Formula: see text]. The derivation operator is then used to give sufficient conditions for the existence of smooth Wigner densities for pairs of operators satisfying the canonical commutation relations. For [Formula: see text], the divergence operator is shown to coincide with the Hud

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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

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35

Kwun, Young Chel, Moquddsa Zahra, Ghulam Farid, Praveen Agarwal та Shin Min Kang. "Some General Integral Operator Inequalities Associated with φ -Quasiconvex Functions". Mathematical Problems in Engineering 2021 (8 січня 2021): 1–11. http://dx.doi.org/10.1155/2021/6696602.

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This paper deals with generalized integral operator inequalities which are established by using φ -quasiconvex functions. Bounds of an integral operator are established which have connections with different kinds of known fractional integral operators. All the results are deducible for quasiconvex functions. Some fractional integral inequalities are deduced.

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36

Kwun, Young Chel, Moquddsa Zahra, Ghulam Farid, Praveen Agarwal та Shin Min Kang. "Some General Integral Operator Inequalities Associated with φ -Quasiconvex Functions". Mathematical Problems in Engineering 2021 (8 січня 2021): 1–11. http://dx.doi.org/10.1155/2021/6696602.

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This paper deals with generalized integral operator inequalities which are established by using φ -quasiconvex functions. Bounds of an integral operator are established which have connections with different kinds of known fractional integral operators. All the results are deducible for quasiconvex functions. Some fractional integral inequalities are deduced.

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37

Chen, Jiecheng, and Guoen Hu. "Compact Commutators of Rough Singular Integral Operators." Canadian Mathematical Bulletin 58, no. 1 (2015): 19–29. http://dx.doi.org/10.4153/cmb-2014-042-1.

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AbstractLet b ∊ BMO(ℝn) and TΩ be the singular integral operator with kernel Ω(x)/|x|n, where Ω is homogeneous of degree zero, integrable, and has mean value zero on the unit sphere Sn-1. In this paper, using Fourier transform estimates and approximation to the operator TΩ by integral operators with smooth kernels, it is proved that if b ∊ CMO(ℝn) and satisfies certain minimal size condition, then the commutator generated by b and TΩ is a compact operator on Lp(ℝn) for appropriate index p. The associated maximal operator is also considered.

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38

Set, Erhan. "Some new generalizations of Ostrowski type inequalities for s-convex functions via fractional integral operators." Filomat 32, no. 16 (2018): 5595–609. http://dx.doi.org/10.2298/fil1816595s.

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Remarkably a lot of Ostrowski type inequalities involving various fractional integral operators have been investigated by many authors. Recently, Raina [34] introduced a new generalization of the Riemann-Liouville fractional integral operator involving a class of functions defined formally by F? ?,?(x)=??,k=0 ?(k)/?(?k + ?)xk. Using this fractional integral operator, in the present note, we establish some new fractional integral inequalities of Ostrowski type whose special cases are shown to yield corresponding inequalities associated with Riemann-Liouville fractional integral operators.

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39

Simsek, Yilmaz. "Some New Families of Special Polynomials and Numbers Associated with Finite Operators." Symmetry 12, no. 2 (2020): 237. http://dx.doi.org/10.3390/sym12020237.

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The aim of this study was to define a new operator. This operator unify and modify many known operators, some of which were introduced by the author. Many properties of this operator are given. Using this operator, two new classes of special polynomials and numbers are defined. Many identities and relationships are derived, including these new numbers and polynomials, combinatorial sums, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the Daehee numbers, and the Changhee numbers. By applying the derivative operator to these new polynomials, derivative formulas are found. Integr

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40

Ignatenko, M. V. "Operator interpolation formulas of Hermitе type with arbitrary multiplicity nodes based on identity transformations of function". Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 54, № 3 (2018): 263–72. http://dx.doi.org/10.29235/1561-2430-2018-54-3-263-272.

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The problem of construction and research of Hermite interpolation formulas with nodes of arbitrary multiplicity for operators given in functional spaces of one and two variables is considered. The construction of operator interpolation polynomials is based both on interpolation polynomials for scalar functions with respect to an arbitrary Chebyshev system and on identity transformations of functions. The reduced operator formulas contain the Stieltjes integrals and the Gateaux differentials of an interpolated operator and are invariant for a special class of operator polynomials of appropriate

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41

Akın, Lütfi. "A New Approach for the Fractional Integral Operator in Time Scales with Variable Exponent Lebesgue Spaces." Fractal and Fractional 5, no. 1 (2021): 7. http://dx.doi.org/10.3390/fractalfract5010007.

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Integral equations and inequalities have an important place in time scales and harmonic analysis. The norm of integral operators is one of the important study topics in harmonic analysis. Using the norms in different variable exponent spaces, the boundedness or compactness of the integral operators are examined. However, the norm of integral operators on time scales has been a matter of curiosity to us. In this study, we prove the equivalence of the norm of the restricted centered fractional maximal diamond integral operator to the norm of the centered fractional maximal diamond integral opera

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Ashikhmin, Sergey S. "On Convolution-Type Operators with Kernels from Modified Morrey Spaces." UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES, no. 2 (222) (June 27, 2024): 4–11. http://dx.doi.org/10.18522/1026-2237-2024-2-4-11.

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We investigate operators of the form MaH, HMa, and Hb, where Ma is the multiplication operator on the function a, H is the integral convolution operator with the kernel h, and Hb is the integral operator with the bounded characteristic b(x,y). It is assumed that the kernel h belongs to the intersection of the Lebesgue and Morrey spaces, and the operators themselves act from the Lebesgue space to the Morrey space. First, using conditions for the precompactness of a set in the Morrey space, we prove the compactness of the operator Ma H, wherein it is assumed that the function a approaches zero a

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Deva, Krishnan, and Swaminathan Mohanaselvi. "Picture Fuzzy Choquet Integral Based Geometric Aggregation Operators and Its Application to Multi Attribute Decision-Making." Mathematical Modelling of Engineering Problems 9, no. 4 (2022): 1043–52. http://dx.doi.org/10.18280/mmep.090422.

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Picture fuzzy set is an extension of intuitionistic fuzzy set, which allows interpreting uncertain data in decision-making problems. This study provides aggregation operators based on Choquet integral, namely Choquet integral picture fuzzy geometric aggregation (CIPFGA) operator and Choquet integral picture fuzzy hybrid geometric aggregation (CIPFHGA) operator with certain properties of these operators are established. We validate the functioning of the operators with illustrative examples. The CIPFHGA operator has an added benefit of combining the weights of positions along with capturing the

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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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Abasov, Nariman Magamedovich, Nonna Anatolevna Dzhusoeva, and Marat Amurkhanovich Pliev. "Diffuse orthogonally additive operators." Sbornik: Mathematics 215, no. 1 (2024): 1–27. http://dx.doi.org/10.4213/sm9909e.

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A regular orthogonally additive operator is a diffuse operator if it is disjoint from all operators in the band generated by the disjointness preserving operators. We present a criterion for principal lateral projections in an order complete vector lattice $E$ to be disjoint. We also state a criterion for a regular orthogonally additive operator to be diffuse. A criterion for the regularity of an integral Urysohn operator acting on ideal spaces of measurable functions is also presented. This criterion is used to show that an integral operator is diffuse. Examples of vector lattices are conside

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Angeloni, Laura, Jürgen Appell, and Simon Reinwand. "Some remarks on Vainikko integral operators in BV type spaces." Bollettino dell'Unione Matematica Italiana 13, no. 4 (2020): 555–65. http://dx.doi.org/10.1007/s40574-020-00248-3.

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AbstractIn this paper we study Vainikko integral operators which are similar to so-called cordial integral operators and contain the classical Hardy operator, the Schur operator, and the Hilbert transform as special cases. For such operators we obtain norm estimates and equalities, mainly in BV type spaces in the sense of Jordan, Wiener, Riesz, and Waterman. Several examples are also discussed.

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Mayer, F. F., M. G. Tastanov, and A. A. Utemisova. "GEOMETRIC PROPERTIES OF THE BERNATSKY INTEGRAL OPERATOR." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 14, no. 4 (2022): 12–19. http://dx.doi.org/10.14529/mmph220402.

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In the geometric theory of complex variable functions, the study of mapping of classes of regular functions using various operators has now become an independent trend. The connection f(z)∈S o⇔ g(z) = zf'(z) ∈ S * of the classes S o and S * of convex and star-shaped functions can be considered as mapping using the differential operator G[f](x) = zf'(z) of class S o to class S * , that is, G: S o → S * or G(S o ) = S * . The impetus for studying this range of issues was M. Bernatsky's assumption that the inverse operator G –1 [f](x), which translates S * → S o and thereby “improves” the propert

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Gül, Erdal, and Abdüllatif Yalçın. "Some integral inequalities through tempered fractional integral operator." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 73, no. 2 (2024): 399–409. http://dx.doi.org/10.31801/cfsuasmas.1387622.

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In this article, we adopt the tempered fractional integral operators to develop some novel Minkowski and Hermite-Hadamard type integral inequalities. Thus, we give several special cases of the integral inequalities for tempered fractional integrals obtained in the earlier works.

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Tilahun, Kelelaw, Hagos Tadessee, and D. L. Suthar. "The Extended Bessel-Maitland Function and Integral Operators Associated with Fractional Calculus." Journal of Mathematics 2020 (June 23, 2020): 1–8. http://dx.doi.org/10.1155/2020/7582063.

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The aim of this paper is to introduce a presumably and remarkably altered integral operator involving the extended generalized Bessel-Maitland function. Particular properties are considered for the extended generalized Bessel-Maitland function connected with fractional integral and differential operators. The integral operator connected with operators of the fractional calculus is also observed. We point out important links to known findings from some individual cases with our key outcomes.

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Pavlakos, Panaiotis K. "Integral representation theorems in partially ordered vector spaces." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 51, no. 2 (1991): 187–215. http://dx.doi.org/10.1017/s1446788700034194.

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AbstractDefining a Radon-type integration process we extend the Alexandroff, Fichtengolts-KantorovichHildebrandt and Riesz integral representation theorems in partially ordered vector spaces.We also identify some classes of operators with other classes of operator-valued set functions, the correspondence between operator and operator-valued set function being given by integration.All these established results can be immediately applied in C* -algebras (especially in W* -algebras and AW* -algebras of type I), in Jordan algebras, in partially ordered involutory (O*-)algebras, in semifields, in q

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