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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MDPI AG
2021-11-01
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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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format | Article |
id | doaj.art-c0c6bf68178341ab84b3bd666ea10c24 |
institution | Directory Open Access Journal |
issn | 2073-8994 |
language | English |
last_indexed | 2024-03-10T05:01:29Z |
publishDate | 2021-11-01 |
publisher | MDPI AG |
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series | Symmetry |
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 |