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Journal articles on the topic 'Do operator'

Author: Grafiati

Published: 9 March 2023

Last updated: 19 July 2025

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1

Rooin, Jamal, Akram Alikhani, and Mohammad Sal Moslehian. "Operator m-convex functions." Georgian Mathematical Journal 25, no. 1 (2018): 93–107. http://dx.doi.org/10.1515/gmj-2017-0045.

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AbstractThe aim of this paper is to present a comprehensive study of operatorm-convex functions. Let{m\in[0,1]}, and{J=[0,b]}for some{b\in\mathbb{R}}or{J=[0,\infty)}. A continuous function{\varphi\colon J\to\mathbb{R}}is called operatorm-convex if for any{t\in[0,1]}and any self-adjoint operators{A,B\in\mathbb{B}({\mathscr{H}})}, whose spectra are contained inJ, we have{\varphi(tA+m(1-t)B)\leq t\varphi(A)+m(1-t)\varphi(B)}. We first generalize the celebrated Jensen inequality for continuousm-convex functions and Hilbert space operators and then use suitable weight functions to give some weighted refinements. Introducing the notion of operatorm-convexity, we extend the Choi–Davis–Jensen inequality for operatorm-convex functions. We also present an operator version of the Jensen–Mercer inequality form-convex functions and generalize this inequality for operatorm-convex functions involving continuous fields of operators and unital fields of positive linear mappings. Employing the Jensen–Mercer operator inequality for operatorm-convex functions, we construct them-Jensen operator functional and obtain an upper bound for it.

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2

Li, Xiaochun, and Fugen Gao. "On Properties of ClassA(n)andn-Paranormal Operators." Abstract and Applied Analysis 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/629061.

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Letnbe a positive integer, and an operatorT∈B(ℋ)is called a classA(n)operator ifT1+n2/1+n≥|T|2andn-paranormal operator ifT1+nx1/1+n≥||Tx||for every unit vectorx∈ℋ, which are common generalizations of classAand paranormal, respectively. In this paper, firstly we consider the tensor products for classA(n)operators, giving a necessary and sufficient condition forT⊗Sto be a classA(n)operator whenTandSare both non-zero operators; secondly we consider the properties forn-paranormal operators, showing that an-paranormal contraction is the direct sum of a unitary and aC.0completely non-unitary contraction.

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3

Wong, M. W. "Minimal and Maximal Operator Theory With Applications." Canadian Journal of Mathematics 43, no. 3 (1991): 617–27. http://dx.doi.org/10.4153/cjm-1991-036-7.

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AbstractLetXbe a complex Banach space andAa linear operator fromXintoXwith dense domain. We construct the minimal and maximal operators of the operatorAand prove that they are equal under reasonable hypotheses on the spaceXand operatorA. As an application, we obtain the existence and regularity of weak solutions of linear equations on the spaceX. As another application we obtain a criterion for a symmetric operator on a complex Hilbert space to be essentially self-adjoint. An application to pseudo-differential operators of the Weyl type is given.

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4

Rosales, Edixo. "Operadores de riesz en el Alglat(T)∩{T}." Revista Bases de la Ciencia. e-ISSN 2588-0764 6, no. 1 (2021): 49. http://dx.doi.org/10.33936/rev_bas_de_la_ciencia.v6i1.2515.

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 En este trabajo X es un espacio de Banach y B(X) denota los operadores acotados. Si T∈B(X), por lat(T) entenderemos los subespacios invariantes por T. Se dice que T es lleno, si (T(M)) ̅=M, para todo M∈lat(T) (la barra indica la clausura en la topología inducida por la norma). Se prueba principalmente el siguiente resultado: Sean X un espacio de Banach y T ∈B(X) acotado por abajo. Sea K ∈Alglat(T)∩{T}' un operador de Riesz. Si K es lleno, entonces T es lleno. Aquí Alglat(T)={S∈B(X):M∈lat(T)⟾M∈lat(S)} y {T}^'={S∈B(X):S∘T=T∘S}.  Palabras clave: Operador lleno, operador de Riesz, operador acotado por abajo.  Abstract In this work X is a Banach space and B(X) denotes the bounded operators. If T ∈B(X), for lat(T) we will understand the invariant subspaces for T. An operator T is full, if (T(M)) ̅=M, for all M∈ latT (the bar indicates the closure in the topology induced by the norm). The following result is true: Let X be a Banach space, T ∈B(X) a bounded below operator and K ∈Alglat(T)∩{T}' a Riesz operator: If K is a full operator, then T is a full operator. Here Alglat(T)={S∈B(X):M∈lat(T)⟾M∈lat(S)} and {T}^'={S∈B(X):S∘T=T∘S}.  Keywords: full operator, Riesz operator, bounded below operator.

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5

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 operator with IHFs in its kernel and classical Riemann Liouville(R-L) fractional integral and derivative operators, the Hilfer fractional derivative operator, the generalized composite fractonal derivate operaor are established. Results established by the authors in [1-3] follow as few interesting and significant special cases of our main results.

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6

Rosales, Edixo. "RESULTADOS SOBRE OPERADORES LLENOS EN ESPACIOS DE HILBERT." Bases de la Ciencia 5, no. 1 (2020): 51–62. https://doi.org/10.5281/zenodo.6904284.

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<strong>RESUMEN</strong> Se prueba, entre otros, el siguiente resultado: Sea T:H→H un operador autoadjunto inyectivo, y K:H→H un operador de Riesz, tal que  K∈Alglat(T)∩{T}'.  Si K:H→H es lleno, entonces T:H→H es lleno.    <strong>Abstract</strong> It is proved here, among other results, the following: Let T:H→H  be a self-adjoint injective operator, and K:H→H a Riesz operator,  such that K∈Alglat(T)∩{T}'. If K:H→H is a full operator, then T:H→H is a full operator.  

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7

Miloslova, A. A., and T. A. Suslina. "Averaging of Higher-Order Parabolic Equations with Periodic Coefficients." Contemporary Mathematics. Fundamental Directions 67, no. 1 (2021): 130–91. http://dx.doi.org/10.22363/2413-3639-2021-67-1-130-191.

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In L2(Rd;Cn), we consider a wide class of matrix elliptic operators A of order 2p (where p2) with periodic rapidly oscillating coefficients (depending on x/). Here 0 is a small parameter. We study the behavior of the operator exponent e-A for 0 and small . We show that the operatore-A converges as 0 in the operator norm in L2(Rd;Cn) to the exponent e-A0 of the effective operator A0. Also we obtain an approximation of the operator exponent e-A in the norm of operators acting from L2(Rd;Cn) to the Sobolev space Hp(Rd; Cn). We derive estimates of errors of these approximations depending on two parameters: and . For a fixed 0 the errors have the exact order O(). We use the results to study the behavior of a solution of the Cauchy problem for the parabolic equation u(x,)= -(A u)(x,)+F(x,) in Rd.

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8

Rosales, Edixo. "RESULTADOS SOBRE OPERADORES LLENOS EN ESPACIOS DE HILBERT." Revista Bases de la Ciencia. e-ISSN 2588-0764 5, no. 1 (2020): 51. http://dx.doi.org/10.33936/rev_bas_de_la_ciencia.v5i1.1686.

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 Se prueba, entre otros, el siguiente resultado: Sea T:H→H un operador autoadjunto inyectivo, y K:H→H un operador de Riesz, tal que K∈Alglat(T)∩{T}'. Si K:H→H es lleno, entonces T:H→H es lleno.  Palabras clave: Operador de Riesz, operador autoadjunto, operador lleno.  Abstract It is proved here, among other results, the following: Let T:H→H be a self-adjoint injective operator, and K:H→H a Riesz operator, such that K∈Alglat(T)∩{T}'. If K:H→H is a full operator, then T:H→H is a full operator.  Keywords: Riesz operator, self-adjoint operator, full operator.  Resumo  O siguiente resultado, entre outros, está provado: Seja T:H→H um operador autoadjunto limitado abaixo, e K:H→H um operador de Riesz, tal qual K∈AlglatT⋂{T}^'. Se K:H→H é um operador completo, então T:H→H é um operador completo. Palavras-chave: operador Riesz, operador autoadjunto completo.

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9

Muxayyo, Muxtor qizi Sharopova. "INTRODUCING "PROGRAM CONTROL OPERATORS" IN THE JAVA PROGRAMMING LANGUAGE." Multidisciplinary Journal of Science and Technology 3, no. 5 (2023): 222–31. https://doi.org/10.5281/zenodo.10423915.

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This article introduces operators in the Java programming language and their functions. Including comparison operator if-else, ternary operators, loop operators for, while, do-while, selection operator switch, break and continue operator. Solutions to problems associated with each operator are shown.

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10

Gunawan, Gunawan, and Erni Widiyastuti. "KARAKTERISTIK OPERATOR PARANORMAL- * QUASI." Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika 3, no. 1 (2022): 256–73. http://dx.doi.org/10.46306/lb.v3i1.114.

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Given Hilbert space H over the fields of . This study aimed to investigate the paranormal- * quasi operators and their properties in Hilbert space. The study resulted the properties of paranormal- * quasi operators, hyponormal operator, class A operator, Class A- * operator, p- hyponormal operator for p > 0, - paranormal operators, compact operator, and the relationship between them

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11

Chetverikov, V. N. "Linear Differential Operators Invertible in the Integro-differential Sense." Mathematics and Mathematical Modeling, no. 4 (December 13, 2019): 20–33. http://dx.doi.org/10.24108/mathm.0419.0000195.

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The paper studies linear differential operators in derivatives with respect to one variable. Such operators include, in particular, operators defined on infinite prolongations of evolutionary systems of differential equations with one spatial variable. In this case, differential operators in total derivatives with respect to the spatial variable are considered. In parallel, linear differential operators with one independent variable are investigated. The known algorithms for reducing the matrix to a stepwise or diagonal form are generalized to the operator matrices of both types. These generalizations are useful at points, where the functions, into which the matrix components are divided when applying the algorithm, are nonzero.In addition, the integral operator is defined as a multi-valued operator that is the right inverse of the total derivative. Linear operators that involve both the total derivatives and the integral operator are called integro-differential. An invertible operator in the integro-differential sense is an operator for which there exists a two-sided inverse integro-differential operator. A description of scalar differential operators that are invertible in this sense is obtained. An algorithm for checking the invertibility in the integro-differential sense of a differential operator and for constructing the inverse integro-differential operator is formulated.The results of the work can be used to solve linear equations for matrix differential operators arising in the theory of evolutionary systems with one spatial variable. Such operator equations arise when describing systems that are integrable by the inverse scattering method, when calculating recursion operators, higher symmetries, conservation laws and symplectic operators, and also when solving some other problems. The proposed method for solving operator equations is based on reducing the matrices defining the operator equation to a stepwise or diagonal form and solving the resulting scalar operator equations.

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12

Wei, Guiwu. "Uncertain Hamacher Aggregation Operators and Their Application to Multiple Attribute Decision Making." International Journal of Decision Support System Technology 10, no. 2 (2018): 40–64. http://dx.doi.org/10.4018/ijdsst.2018040103.

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This article utilizes Hamacher operations to develop some uncertain aggregation operators: uncertain Hamacher weighted average (UHWA) operator, uncertain Hamacher weighted geometric (UHWG) operator, uncertain Hamacher ordered weighted average (UHOWA) operator, uncertain Hamacher ordered weighted geometric (UHOWG) operator, uncertain Hamacher hybrid average (UHHA) operator, uncertain Hamacher hybrid geometric (UHHG) operator and some uncertain Hamacher correlate aggregation operators and uncertain induced Hamacher aggregation operators. The prominent characteristics of these proposed operators are studied. Then, the article utilizes these operators to develop some approaches to solve the uncertain multiple attribute decision making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

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13

Jana, Suvendu, Pintu Bhunia, and Kallol Paul. "Euclidean operator radius inequalities of d-tuple operators and operator matrices." Mathematica Slovaca 74, no. 4 (2024): 947–62. http://dx.doi.org/10.1515/ms-2024-0070.

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Abstract We study Euclidean operator radius inequalities of d-tuple operators as well as the sum and the product of d-tuple operators. A power inequality for the Euclidean operator radius of d-tuple operators is also studied. Further, we study the Euclidean operator radius inequalities of 2 × 2 operator matrices whose entries are d-tuple operators.

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14

BHOLA, JYOTI, and BHAWNA GUPTA. "Properties of (C, r)-Hankel Operators and (R, r)-Hankel Operators on Hilbert Spaces." Kragujevac Journal of Mathematics 49, no. 6 (2024): 873–87. http://dx.doi.org/10.46793/kgjmat2506.873b.

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We introduce the operators which are generalizations of Hankel-type operators, called the (C,r)-Hankel operator and (R,r)-Hankel operator on general Hilbert spaces. Our main result is to obtain characterizations for a bounded operator on general Hilbert spaces to be a (C,r)-Hankel operator (or (R,r)-Hankel operator). We also discuss some algebraic properties like boundedness (for |r|≠1) of these operators and the relationship between them. Moreover, some characterizations for the commutativity of these operators are explored.

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15

Alomari, Mohammad W., Christophe Chesneau, and Ahmad Al-Khasawneh. "Operator Jensen’s Inequality for Operator Superquadratic Functions." Axioms 11, no. 11 (2022): 617. http://dx.doi.org/10.3390/axioms11110617.

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In this work, an operator superquadratic function (in the operator sense) for positive Hilbert space operators is defined. Several examples with some important properties together with some observations which are related to the operator convexity are pointed out. A general Bohr’s inequality for positive operators is thus deduced. A Jensen-type inequality is proved. Equivalent statements of a non-commutative version of Jensen’s inequality for operator superquadratic function are also established. Finally, several trace inequalities for superquadratic functions (in the ordinary sense) are provided as well.

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16

Rashid, Mohammad H. M., and Wael Mahmoud Mohammad Salameh. "Inequalities for the Euclidean Operator Radius of n-Tuple Operators and Operator Matrices in Hilbert C∗-Modules." Symmetry 16, no. 6 (2024): 647. http://dx.doi.org/10.3390/sym16060647.

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This study takes a detailed look at various inequalities related to the Euclidean operator radius. It examines groups of n-tuple operators, studying how they add up and multiply together. It also uncovers a unique power inequality specific to the Euclidean operator radius. The research broadens its scope to analyze how n-tuple operators, when used as parts of 2×2 operator matrices, illustrate inequalities connected to the Euclidean operator radius. By using the Euclidean numerical radius and Euclidean operator norm for n-tuple operators, the study introduces a range of new inequalities. These inequalities not only set limits for the addition, multiplication, and Euclidean numerical radius of n-tuple operators but also help in establishing inequalities for the Euclidean operator radius. This process involves carefully examining the Euclidean numerical radius inequalities of 2×2 operator matrices with n-tuple operators. Additionally, a new inequality is derived, focusing specifically on the Euclidean operator norm of 2×2 operator matrices. Throughout, the research keeps circling back to the idea of finding and understanding symmetries in linear operators and matrices. The paper highlights the significance of symmetry in mathematics and its impact on various mathematical areas.

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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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Rashid, M. H. M., and Rabaa Al-Maita. "Discrepancies in Euclidean Operator Radii in Hilbert C∗-Modules." International Journal of Analysis and Applications 22 (October 2, 2024): 174. http://dx.doi.org/10.28924/2291-8639-22-2024-174.

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In this research, we establish precise limits for the Euclidean operator radius of two bounded linear operators operating within a Hilbert C∗-module over A. Furthermore, our work establishes a connection between these limits and recent research findings that provide accurate upper and lower bounds for the numerical radius of linear operators. The primary objective of this investigation is to explore various specific scenarios of interest and extend existing inequalities found in the literature to encompass the Euclidean radius of two operators in a Hilbert A-module. Additionally, our study presents conclusions that reveal relationships between the operator norm, the typical numerical radius of a composite operator, and the Euclidean operator radius. Furthermore, we introduce several new inequalities involving the Euclidean numerical radius and Euclidean operator norm of 2-tuple operators. These inequalities offer both lower and upper bounds for the Euclidean numerical radius of 2-tuple operators, as well as for the sum and product of 2-tuple operators. We also delve into the study of Euclidean numerical radius inequalities for 2×2 operator matrices whose entries consist of 2-tuple operators, leading to the derivation of some Euclidean operator radius inequalities. Additionally, we establish an inequality for the Euclidean operator norm of 2×2 operator matrices.

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19

Rosales, Edixo. "Operadores de riesz en el Alglat(T)∩{T}." Bases de la Ciencia 6, no. 1 (2021): 49–56. https://doi.org/10.5281/zenodo.6991278.

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<strong>RESUMEN</strong> En este trabajo X es un espacio de Banach y B(X) denota los operadores acotados. Si T∈B(X), por lat(T) entenderemos los subespacios invariantes por T. Se dice que T es lleno, si (T(M)) ̅=M, para todo M∈lat(T) (la barra indica la clausura en la topología inducida por la norma). Se prueba principalmente el siguiente resultado: Sean X un espacio de Banach y T ∈B(X) acotado por abajo. Sea K ∈Alglat(T)∩{T}' un operador de Riesz. Si K es lleno, entonces T es lleno. Aquí Alglat(T)={S∈B(X):M∈lat(T)⟾M∈lat(S)} y {T}^'={S∈B(X):S∘T=T∘S}.      <strong>Abstract</strong>  In this work X is a Banach space and B(X) denotes the bounded operators. If T ∈B(X), for lat(T) we will understand the invariant subspaces for T. An operator T is full, if (T(M)) ̅=M, for all M∈ latT (the bar indicates the closure in the topology induced by the norm). The following result is true: Let X be a Banach space, T ∈B(X) a bounded below operator and K ∈Alglat(T)∩{T}' a Riesz operator: If K is a full operator, then T is a full operator. Here Alglat(T)={S∈B(X):M∈lat(T)⟾M∈lat(S)} and {T}^'={S∈B(X):S∘T=T∘S}.   

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20

Wang, Li Yuan, and Kai Kang. "Research and Analysis of Edge-Detection of Digital Images." Applied Mechanics and Materials 263-266 (December 2012): 2538–41. http://dx.doi.org/10.4028/www.scientific.net/amm.263-266.2538.

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Edge-detection is the basic characteristic of images. Edge-detection plays an important role in computer vision and image analysis, it is the key link of image analysis and recognition. In this paper, we mainly analyze several edge-detection operators, research the processing results. The edge-detection operators mainly include Roberts operator, Prewitt operator, Sobel operator, Canny operator and LoG operator. Finally we discuss the advantage and disadvantage of the edge-detection operators.

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21

Mahmood Kamil Shihab. "Generalization of Fuglede-Putnam Theorem to (p, q)−Quasiposinormal Operator and (p, q)− Co-posinormal Operator." Tikrit Journal of Pure Science 21, no. 3 (2023): 184–86. http://dx.doi.org/10.25130/tjps.v21i3.1014.

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In this paper we generalize the Fuglede-Putnam theorem to non-normal operators to posinormal operator and co-posinormal operators. Also we prove this theorem to supra class posinormal operators (called supraposinormal operator) and co-supra class posinormal operators (called cosupraposinormal operator).

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22

Journal, Baghdad Science. "Quasi-posinormal operators." Baghdad Science Journal 7, no. 3 (2010): 1282–87. http://dx.doi.org/10.21123/bsj.7.3.1282-1287.

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In this paper, we introduce a class of operators on a Hilbert space namely quasi-posinormal operators that contain properly the classes of normal operator, hyponormal operators, M–hyponormal operators, dominant operators and posinormal operators . We study some basic properties of these operators .Also we are looking at the relationship between invertibility operator and quasi-posinormal operator .

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23

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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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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Berkani, M., and N. Castro-González. "UNBOUNDED B-FREDHOLM OPERATORS ON HILBERT SPACES." Proceedings of the Edinburgh Mathematical Society 51, no. 2 (2008): 285–96. http://dx.doi.org/10.1017/s0013091505001574.

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AbstractThis paper is concerned with the study of a class of closed linear operators densely defined on a Hilbert space $H$ and called B-Fredholm operators. We characterize a B-Fredholm operator as the direct sum of a Fredholm closed operator and a bounded nilpotent operator. The notion of an index of a B-Fredholm operator is introduced and a characterization of B-Fredholm operators with index $0$ is given in terms of the sum of a Drazin closed operator and a finite-rank operator. We analyse the properties of the powers $T^m$ of a closed B-Fredholm operator and we establish a spectral mapping theorem.

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26

Lin, C. S. "On operator order and chaotic operator order for two operators." Linear Algebra and its Applications 425, no. 1 (2007): 1–6. http://dx.doi.org/10.1016/j.laa.2007.02.030.

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Fomin, Vasiliy I. "About a complex operator resolvent." Russian Universities Reports. Mathematics, no. 138 (2022): 183–97. http://dx.doi.org/10.20310/2686-9667-2022-27-138-183-197.

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A normed algebra of bounded linear complex operators acting in a complex normed space consisting of elements of the Cartesian square of a real Banach space is constructed. In this algebra, it is singled out a set of operators for each of which the real and imaginary parts commute with each other. It is proved that in this set, any operator for which the sum of squares of its real and imaginary parts is a continuously invertible operator, is invertible itself; a formula for the inverse operator is found. For an operator from the indicated set, the form of its regular points is investigated: conditions under which a complex number is a regular point of the given operator are found; a formula for the resolvent of a complex operator is obtained. The set of unbounded linear complex operators acting in the above complex normed space is considered. In this set, a subset of those operators for each of which the domains of the real and imaginary parts coincide is distinguished. For an operator from the specified subset, conditions on a complex number under which this number belongs to the resolvent set of the given operator are found; a formula for the resolvent of the operator is obtained. The concept of a semi-bounded complex operator as an operator in which one component is a bounded and the other is an unbounded operator is introduced. It is noted that the first and second resolvent identities for complex operators can be proved similarly to the case of real operators.

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Čatipović, Marija, and Saša Krešić-Jurić. "Sturm-Liouvilleov problem." Acta mathematica Spalatensia. Series didactica 4, no. 4 (2021): 97–111. http://dx.doi.org/10.32817/amssd.4.4.7.

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Klasična Sturm-Liouvilleova jednadžba, nazvana po Jacquesu Sturmu i Josephu Liouvilleu, je obična diferencijalna jednadžba drugog reda posebnog oblika u ovisnosti o parametru lambda. Pronalaženje te vrijednosti za koju postoje netrivijalna rješenja jednadžbe i koja zadovoljavaju rubne uvjete je dio problema kojeg nazivamo Sturm-Liouvilleov problem. Pokazat ćemo da se proizvoljni linearni operator drugog reda može transformirati u Sturm-Liouvilleov operator tj. da je Sturm-Liouvilleov operator kanonski oblik diferencijalnog operatora drugog reda. Vlastite vrijednosti regularnog Sturm-Liouvilleovog problema su realne, prebrojive i tvore strogo rastući neomeđeni niz. Također, za svaku vlastitu vrijednost postoji odgovarajuća vlastita funkcija jedinstveno određena do na multiplikativnu konstantu koja ima točno n nultočki u intervalu [a; b]. Ovo je jedan od fundamentalnih rezlutata za Sturm-Liouvilleove operatore.

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Dakheel, Shireen O., and Buthainah A. Ahmed. "C₁ C₂- symmetric operators for some types of operators." Journal of Physics: Conference Series 2322, no. 1 (2022): 012051. http://dx.doi.org/10.1088/1742-6596/2322/1/012051.

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Abstract In this paper, we give some new properties of C1C2-symmetric operators and discuss some results about these kind of operators. Also, we describe the conditions that a binormal operator becomes normal operator and give necessary and sufficient conditions that C1C2- symmetric operators becomes a binormal operator. Finally, we solve the problem that a binormal operator is not closed under addition.

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30

Mahmoud, Sid Ahmed Ould Ahmed, El Moctar Ould Beiba, Sidi Hamidou Jah, and Maawiya Ould Sidi. "Structure of k -Quasi- m , n -Isosymmetric Operators." Journal of Mathematics 2022 (September 26, 2022): 1–13. http://dx.doi.org/10.1155/2022/8377463.

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The investigation of new operators belonging to some specific classes has been quite fashionable since the beginning of the century, and sometimes it is indeed relevant. In this study, we introduce and study a new class of operators called k -quasi- m , n -isosymmetric operators on Hilbert spaces. This new class of operators emerges as a generalization of the m , n -isosymmetric operators. We give a characterization for any operator to be k -quasi- m , n -isosymmetric operator. Using this characterization, we prove that any power of an k -quasi- m , n -isosymmetric operator is also an k -quasi- m , n -isosymmetric operator. Furthermore, we study the perturbation of an k -quasi- m , n -isosymmetric operator with a nilpotent operator. The product and tensor products of two k -quasi- m , n -isosymmetries are investigated.

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31

Yang, Yixuan, Yuchao Tang, and Chuanxi Zhu. "Iterative Methods for Computing the Resolvent of Composed Operators in Hilbert Spaces." Mathematics 7, no. 2 (2019): 131. http://dx.doi.org/10.3390/math7020131.

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The resolvent is a fundamental concept in studying various operator splitting algorithms. In this paper, we investigate the problem of computing the resolvent of compositions of operators with bounded linear operators. First, we discuss several explicit solutions of this resolvent operator by taking into account additional constraints on the linear operator. Second, we propose a fixed point approach for computing this resolvent operator in a general case. Based on the Krasnoselskii–Mann algorithm for finding fixed points of non-expansive operators, we prove the strong convergence of the sequence generated by the proposed algorithm. As a consequence, we obtain an effective iterative algorithm for solving the scaled proximity operator of a convex function composed by a linear operator, which has wide applications in image restoration and image reconstruction problems. Furthermore, we propose and study iterative algorithms for studying the resolvent operator of a finite sum of maximally monotone operators as well as the proximal operator of a finite sum of proper, lower semi-continuous convex functions.

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32

Fomin, Vasiliy I. "About unbounded complex operators." Russian Universities Reports. Mathematics, no. 129 (2020): 57–67. http://dx.doi.org/10.20310/2686-9667-2020-25-129-57-67.

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The concept of an unbounded complex operator as an operator acting in the pull-back of a Banach space is introduced. It is proved that each such operator is linear. Linear operations of addition and multiplication by a number and also the operation of multiplication are determined on the set of unbounded complex operators. The conditions for commutability of operators from this set are indicated. The product of complex conjugate operators and the properties of the conjugation operation are considered. Invertibility questions are studied: two contractions of an unbounded complex operator that have an inverse operator are proposed, and an explicit form of the inverse operator is found for one of these restrictions. It is noted that unbounded complex operators can ﬁnd application in the study of a linear homogeneous diﬀerential equation with constant unbounded operator coeﬃcients in a Banach space.

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33

A.M, Wafula, and Mogoi N. Evans. "Norm-Attainable Operators in Operator Ideals: Characterizations, Properties, and Structural Implications." Asian Research Journal of Mathematics 20, no. 12 (2024): 119–24. https://doi.org/10.9734/arjom/2024/v20i12879.

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This paper explores the interplay between norm-attainable operators and operator ideals in the context of Hilbert spaces, providing a comprehensive characterization of their structural and geometric properties. We investigate norm-attainability within common operator classes, including compact operators, Schatten (p)- class, trace-class, and weakly compact operators. Foundational lemmas establish the existence and basic properties of norm-attainable operators, which are extended through propositions detailing their behavior under inclusion in specific operator ideals. Key theorems characterize conditions for norm-attainability, highlighting connections to compactness, spectral properties, and finite-rank approximations. The results elucidate practical implications, such as operator approximations and eigenvalue relationships. These findingshave direct applications in quantum mechanics, signal processing, and numerical analysis, where operator approximations are crucial for efficient computation and system modeling. Furthermore, we outline potential extensions of this work to the more general settings of unbounded operators and Banach spaces, opening avenues for future research and broadening the scope of applicability. This study advances understanding of norm-attainable operators in operator theory, offering new insights into their algebraic and geometric significance within operator ideals.

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34

Wang, Rui, Jie Wang, Hui Gao, and Guiwu Wei. "Methods for MADM with Picture Fuzzy Muirhead Mean Operators and Their Application for Evaluating the Financial Investment Risk." Symmetry 11, no. 1 (2018): 6. http://dx.doi.org/10.3390/sym11010006.

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In this article, we study multiple attribute decision-making (MADM) problems with picture fuzzy numbers (PFNs) information. Afterwards, we adopt a Muirhead mean (MM) operator, a weighted MM (WMM) operator, a dual MM (DMM) operator, and a weighted DMM (WDMM) operator to define some picture fuzzy aggregation operators, including the picture fuzzy MM (PFMM) operator, the picture fuzzy WMM (PFWMM) operator, the picture fuzzy DMM (PFDMM) operator, and the picture fuzzy WDMM (PFWDMM) operator. Of course, the precious merits of these defined operators are investigated. Moreover, we have adopted the PFWMM and PFWDMM operators to build a decision-making model to handle picture fuzzy MADM problems. In the end, we take a concrete instance of appraising a financial investment risk to demonstrate our defined model and to verify its accuracy and scientific merit.

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35

Lehner, Franz. "Free operators with operator coefficients." Colloquium Mathematicum 74, no. 2 (1998): 321–28. http://dx.doi.org/10.4064/cm-74-2-321-328.

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36

Menkad, Safa, and Ameur Seddik. "Operator inequalities and normal operators." Banach Journal of Mathematical Analysis 6, no. 2 (2012): 204–10. http://dx.doi.org/10.15352/bjma/1342210170.

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37

Pinchover, Yehuda. "shuttle operator for elliptic operators." Duke Mathematical Journal 85, no. 2 (1996): 431–45. http://dx.doi.org/10.1215/s0012-7094-96-08518-x.

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38

Ando, Tsuyoshi, and Chi-Kwong Li. "Operator radii and unitary operators." Operators and Matrices, no. 2 (2010): 273–81. http://dx.doi.org/10.7153/oam-04-14.

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39

McKeon, D. G. C. "Operator regularization and composite operators." Canadian Journal of Physics 68, no. 3 (1990): 296–300. http://dx.doi.org/10.1139/p90-047.

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We demonstrate how operator regularization can be used to compute radiative corrections to Green's functions involving composite operators. No divergences are encountered and no symmetry-breaking regulating parameter need be introduced into the initial Lagrangian. We demonstrate the technique to one-loop order by considering operators of dimension four in the [Formula: see text] model and the operator [Formula: see text] in an axial model. Anomalous dimensions of these operators are determined by considering finite Green's functions. There is no need to define "oversubtracted" operators to maintain linearity, as is the case when one uses BPH subtraction, nor is there an ambiguity between the trace of [Formula: see text] and [Formula: see text], as occurs in dimensional regularization. Quantities such as γ5, εμνλσ, and εμν (which are well-defined only in an integer number of dimensions) are treated unambiguously as we never alter the dimensionality of the problem.

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40

Nowak, Marian. "Operator measures and integration operators." Indagationes Mathematicae 24, no. 1 (2013): 279–90. http://dx.doi.org/10.1016/j.indag.2012.10.002.

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41

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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42

Bracic, Janko. "Arens regularity andweakly compact operators." Filomat 32, no. 14 (2018): 4993–5002. http://dx.doi.org/10.2298/fil1814993b.

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We explore the relation between Arens regularity of a bilinear operator and the weak compactness of the related linear operators. Since every bilinear operator has natural factorization through the projective tensor product a special attention is given to Arens regularity of the tensor operator. We consider topological centers of a bilinear operator and we present a few results related to bilinear operators which can be approximated by linear operators.

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43

Dimitrijevic, Mirjana, and Snezana Zivkovic-Zlatanovic. "Essentially left and right generalized Drazin invertible operators and generalized Saphar decomposition." Filomat 37, no. 28 (2023): 9511–29. http://dx.doi.org/10.2298/fil2328511d.

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In this paper we define and study the classes of the essentially left and right generalized Drazin invertible operators and of the left and rightWeyl-g-Drazin invertible operators by means of the analytical core and the quasinilpotent part of an operator. We show that the essentially left (right) generalized Drazin invertible operator can be represented as a sum of a left (right) Fredholm and a quasinilpotent operator. Analogously, the left (right) Weyl-g-Drazin invertible operator can be represented as a sum of a left (right) Weyl and a quasinilpotent operator. We also characterize these operators in terms of their generalized Saphar decompositions, accumulation and interior points of various spectra of operator pencils. Furthermore, we expand the results from [10], on the left and right generalized Drazin invertible operators. Special attention is devoted to the investigation of the corresponding spectra of operator pencils.

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44

Laith K. Shaakir and Saad S. Marai. "quasi-normal Operator of order n." Tikrit Journal of Pure Science 20, no. 4 (2023): 167–69. http://dx.doi.org/10.25130/tjps.v20i4.1231.

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In this paper, we introduce a new class of operators acting on a complex Hilbert space H which is called quasi-normal operator of order n. An operator T∈B(H) is called quasi-normal operator of order n if T(T*n Tn)=(T*n Tn)T, where n is positive integer number greater than 1 and T* is the adjoint of the operator T, We investigate some basic properties of such operators and study relations among quasi-normal operator of order n and some other operators.

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45

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 considered in which the sets of diffuse operators consist only of the zero element. The general form of an order projection operator onto the band generated by the disjointness preserving operators is found. Bibliography: 47 titles.

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46

Chen, Dazhao, and Hui Huang. "Sharp function estimates and boundedness for Toeplitz-type operators associated with general fractional integral operators." Open Mathematics 19, no. 1 (2021): 1554–66. http://dx.doi.org/10.1515/math-2021-0122.

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Abstract In this paper, we establish some sharp maximal function estimates for certain Toeplitz-type operators associated with some fractional integral operators with general kernel. As an application, we obtain the boundedness of the Toeplitz-type operators on the Lebesgue, Morrey and Triebel-Lizorkin spaces. The operators include the Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.

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47

Evans, Mogoi N., and Robert obogi. "The geometry and norm-attainability of operators in operator ideals: the role of singular values and compactness." Open Journal of Mathematical Analysis 8, no. 2 (2024): 79–88. https://doi.org/10.30538/psrp-oma2024.0145.

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This paper investigates the geometry and norm-attainability of operators within various operator ideals, with a particular focus on the role of singular values and compactness. We explore the behavior of norm-attainable operators in the context of classical operator ideals, such as trace-class and Hilbert-Schmidt operators, and examine how their geometric and algebraic properties are influenced by membership in these ideals. A key result of this study is the connection between the singular values of trace-class operators and their operator norm, establishing a foundational relationship for understanding norm-attainment. Additionally, we explore the conditions under which weakly compact and compact operators can attain their operator norm, providing further insights into the structural properties that govern norm-attainability in operator theory. The findings contribute to a deeper understanding of the interplay between operator ideals and norm-attainability, with potential applications in functional analysis and related fields.

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48

Elaf Sabah Abdulwahid Rijab. "Triple Operators of Order n on a Hilbert Space." Tikrit Journal of Pure Science 23, no. 3 (2018): 151–53. http://dx.doi.org/10.25130/tjps.v23i3.512.

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In this paper, we introduce a new class of operators on a complex Hilbert space which is called triple operators of order n. An operator is called triple operator of order n if where is the adjoint of the operator . We investigate some basic properties of such operators and study the relation between the triple operators of order n and some kinds of operators.

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49

Beanland, Kevin, and Ryan M. Causey. "Genericity and Universality for Operator Ideals." Quarterly Journal of Mathematics 71, no. 3 (2020): 1081–129. http://dx.doi.org/10.1093/qmathj/haaa018.

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Abstract A bounded linear operator $U$ between Banach spaces is universal for the complement of some operator ideal $\mathfrak{J}$ if it is a member of the complement and it factors through every element of the complement of $\mathfrak{J}$. In the first part of this paper, we produce new universal operators for the complements of several ideals, and give examples of ideals whose complements do not admit such operators. In the second part of the paper, we use descriptive set theory to study operator ideals. After restricting attention to operators between separable Banach spaces, we call an operator ideal $\mathfrak{J}$ generic if whenever an operator $A$ has the property that every operator in $\mathfrak{J}$ factors through a restriction of $A$, then every operator between separable Banach spaces factors through a restriction of $A$. We prove that many classical operator ideals (such as strictly singular, weakly compact, Banach–Saks) are generic and give a sufficient condition, based on the complexity of the ideal, for when the complement does not admit a universal operator. Another result is a new proof of a theorem of M. Girardi and W. B. Johnson, which states that there is no universal operator for the complement of the ideal of completely continuous operators.

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50

Sharma, Poonam, Ravinder Krishna Raina, and Janusz Sokół. "On a Generalized Convolution Operator." Symmetry 13, no. 11 (2021): 2141. http://dx.doi.org/10.3390/sym13112141.

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Recently in the paper [Mediterr. J. Math. 2016, 13, 1535–1553], the authors introduced and studied a new operator which was defined as a convolution of the three popular linear operators, namely the Sǎlǎgean operator, the Ruscheweyh operator and a fractional derivative operator. In the present paper, we consider an operator which is a convolution operator of only two linear operators (with lesser restricted parameters) that yield various well-known operators, defined by a symmetric way, including the one studied in the above-mentioned paper. Several results on the subordination of analytic functions to this operator (defined below) are investigated. Some of the results presented are shown to involve the familiar Appell function and Hurwitz–Lerch Zeta function. Special cases and interesting consequences being in symmetry of our main results are also mentioned.

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