On a Generalized Convolution Operator

Recently in the paper [<i>Mediterr. J. Math.</i> <b>2016</b>, <i>13</i>, 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 a...

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Main Authors: Poonam Sharma, Ravinder Krishna Raina, Janusz Sokół
Format: Article
Language:English
Published: MDPI AG 2021-11-01
Series:Symmetry
Subjects:
Online Access:https://www.mdpi.com/2073-8994/13/11/2141
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author Poonam Sharma
Ravinder Krishna Raina
Janusz Sokół
author_facet Poonam Sharma
Ravinder Krishna Raina
Janusz Sokół
author_sort Poonam Sharma
collection DOAJ
description Recently in the paper [<i>Mediterr. J. Math.</i> <b>2016</b>, <i>13</i>, 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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spelling doaj.art-c0c6bf68178341ab84b3bd666ea10c242023-11-23T01:45:42ZengMDPI AGSymmetry2073-89942021-11-011311214110.3390/sym13112141On a Generalized Convolution OperatorPoonam Sharma0Ravinder Krishna Raina1Janusz Sokół2Department of Mathematics and Astronomy, University of Lucknow, Lucknow 226007, IndiaDepartment of Mathematics, College of Technology & Engineering, M.P. University of Agriculture and Technology, Udaipur 313002, IndiaCollege of Natural Sciences, University of Rzeszów, Ul. Prof. Pigonia 1, 35-310 Rzeszów, PolandRecently in the paper [<i>Mediterr. J. Math.</i> <b>2016</b>, <i>13</i>, 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.https://www.mdpi.com/2073-8994/13/11/2141analytic functionsconvolutionsubordinationconvex functions
spellingShingle Poonam Sharma
Ravinder Krishna Raina
Janusz Sokół
On a Generalized Convolution Operator
Symmetry
analytic functions
convolution
subordination
convex functions
title On a Generalized Convolution Operator
title_full On a Generalized Convolution Operator
title_fullStr On a Generalized Convolution Operator
title_full_unstemmed On a Generalized Convolution Operator
title_short On a Generalized Convolution Operator
title_sort on a generalized convolution operator
topic analytic functions
convolution
subordination
convex functions
url https://www.mdpi.com/2073-8994/13/11/2141
work_keys_str_mv AT poonamsharma onageneralizedconvolutionoperator
AT ravinderkrishnaraina onageneralizedconvolutionoperator
AT januszsokoł onageneralizedconvolutionoperator