Distortion and Convolutional Theorems for Operators of Generalized Fractional Calculus Involving Wright Function

Abstract

Using the Wright's generalized hypergeometric function, we investigate a class W (q, s; A, B, λ) of analytic functions with negative coefficients. We derive many results for the modified Hadamard product of functions belonging to the class W (q, s; A, B, λ). Moreover, we generalize some of the distortion theorems to the classical fractional integrals and derivatives and the Saigo (hypergeometric) operators of fractional calculus.2000 Mathematics Subject Classification. Primary: 30C45, 26A33.

On Parametric p-Valent Meromorphic Functions

“…where, q+1 ψ q (z) is Wright's (psi) function which is a generalized hypergeometric function (Srivastava and Manocha, 1984) and its series representation is given by: ([a 1 , A 1 ])f, is itself a generalized operator and is a meromorphic version of the operator considered in Aouf and Dziok, 2008a;2008b;Sharma, 2010;. Taking A i = B i = 1, i = 1,2,…,q, q+1 ψ q (z) reduces to the generalized hypergeometric function q +1 F q and we denote:…”

Applications of differential subordinations involving a generalized fractional differintegral operator

“…Using the above defined function, Tang et al [24] (see also Aouf et al [4,7] and [8]) defined the operator H λ,δ p,η,μ :…”

Certain Subclasses of Multivalent Analytic Functions

“…Analytic functions which are starlike with respect to symmetric points and related functions have been extensively investigated in [1][2][3][4][5][6]. Recently, several authors have obtained many important properties and characteristics of multivalent analytic functions (see, e.g., [7][8][9][10][11]). The main object of this paper is to present some distortion inequalities of functions in the classes , ( , , ) and , ( , , ) which we have introduced here.…”