Inequalities of harmonic univalentfunctions with connectionsof hypergeometric functions : Open Mathematics

摘要

Let SH be the class of functions f = h+g that are harmonic univalent and sense-preserving in the openunit disk U = { z : |z| < 1} for which f (0) = f'(0)-1=0. In this paper, we introduce and study a subclassH( α, β) of the class SH and the subclass NH( α, β) with negative coefficients. We obtain basic results involvingsufficient coefficient conditions for a function in the subclass H( α, β) and we show that these conditions are alsonecessary for negative coefficients, distortion bounds, extreme points, convolution and convex combinations. In thispaper an attempt has also been made to discuss some results that uncover some of the connections of hypergeometricfunctions with a subclass of harmonic univalent functions.