Generalized convolution properties based on the modified Mittag-Leffler function

Abstract

Studies of convolution play an important role in Geometric Function Theory (GFT). Such studies attracted a large number of researchers in recent years. By making use of the Hadamard product (or convolution), several new and interesting subclasses of analytic and univalent functions have been introduced and investigated in the direction of well-known concepts such as the subordination and superordination inequalities, integral mean and partial sums, and so on. In this article, we apply the Hadamard product (or convolution) by utilizing some special functions. Our contribution in this paper includes defining a new linear operator in the form of the generalized Mittag-Leffler function in terms of the extensively-investigated Fox-Wright p Ψ qfunction in the right-half of the open unit disk where where (z) > 0. We then show that the new linear convolution operator is bounded in some spaces. In particular, several boundedness properties of this linear convolution operator under mappings from a weighted Bloch space into a weighted-log Bloch space are also investigated. For uniformity and convenience, the Fox-Wright p Ψ q -notation is used in our results.

Geometric Properties of Normalized Mittag–Leffler Functions

“…The interested readers are suggested to go through [6][7][8][9]. Let A be the family of all functions g having the form…”

Second Hankel determinant for a class defined by modified Mittag-Leffler with generalized polylogarithm functions

“…where M m α,β,λ f(z) is a new generalized operator from convolution between the linear operator of the generalized Mittag-Leffler function in term of the extensively-investigated Fox-Wright p Ψ q function introduced by Srivastava et. al [20] and the generalized polylogarithm functions D m λ f(z) introduced by Al-Saqsi and Darus [4].…”

Inclusion and convolution features of univalent meromorphic functions correlating with Mittag-Leffler function

“…The following year, Srivastava and Bansal [33] studied a certain class of q-M-LF and investigated sufficient conditions under which it is close-to-convex. At the same time, Srivastava et al [34] imposed a new convolution operator in the form of the generalized M-LF based on the extensively-studied Fox-Wright function in the right-half of the open unit disk where (z) > 0. In 2018, Kumar, Choi and Srivastava [17] investigated the solution of the generalized fractional kinetic equation involving another generalized M-LF by applying the Sumudu transform and the Laplace transform techniques.…”