Symmetry (Nov 2021)

On a Generalized Convolution Operator

  • Poonam Sharma,
  • Ravinder Krishna Raina,
  • Janusz Sokół

DOI
https://doi.org/10.3390/sym13112141
Journal volume & issue
Vol. 13, no. 11
p. 2141

Abstract

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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.

Keywords