On a Generalized Convolution Operator

Symmetry

Janusz Sokół¹  Poonam Sharma²  Ravinder Krishna Raina³ 

[1] College of Natural Sciences, University of Rzeszów, Ul. Prof. Pigonia 1, 35-310 Rzeszów, Poland;Department of Mathematics and Astronomy, University of Lucknow, Lucknow 226007, India;Department of Mathematics, College of Technology & Engineering, M.P. University of Agriculture and Technology, Udaipur 313002, India;

关键词: analytic functions;    convolution;    subordination;    convex functions;   

DOI  :  10.3390/sym13112141

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown