Certain Class of P-Valent Functions Associated With the Wright Generalized Hypergeometric Function

Abstract

Abstract.Using the Wright's generalized hypergeometric function, we introduce a new class Wk (p,q,s; A, B, A) of analytic p-valent functions with negative coefficients. In this paper we investigate coefficients estimates, distortion theorem, the radii of p-valent starlikeness and p-valent convexity and modified Hadamard products.

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:…”

Extremal problems in the class of analytic functions associated with Wright's function

“…The afore-mentioned definitions are fairly well known (see, for example [1,3,4,[9][10][11][12][16][17][18] where n is defined by n D ! .˛1 C A 1 .n p// .˛q C A q .n p// .ˇ1 C B 1 .n p// .ˇs C B s .n p//.n p/Š (6) and !…”

“…Many interesting subclasses of analytic functions associated with the linear operator (4) and its various special cases were investigated recently in [1,3,5,6].…”

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

“…The Wright generalized hypergeometric functions (2) have been recently involved in the geometric function theory, see [1], [2], [3], [14], [15] and [16], as well as: [7], [8], [9] and [13]. It is a special case of Fox's function (see for example [6], [12] and [19]).…”

“…Using the linear operator θ[α 1 ] Aouf and Dziok [1] defined the class W (q, s; A, B, λ) of functions of the form…”