Some Fox-Wright generalized hypergeometric functions and associated families of convolution operators

Abstract

Here, in this lecture, we aim at presenting a systematic account of the basic properties and characteristics of several subclasses of analytic functions (with Montel’s normalization), which are based upon some convolution operators on Hilbert space involving the Fox-Wright generalization of the classical hypergeometric qFs function (with q numerator and s denominator parameters). The various results presented in this lecture include (for example) normed coefficient inequalities and estimates, distortion theorems, and the radii of convexity and starlikeness for each of the analytic function classes which are investigated here. We also briefly indicate the relevant connections of the some of the results considered here with those involving the Dziok-Srivastava operator.