Sufficiency for Gaussian hypergeometric functions to be uniformly convex
type: Item
instance of: scholarly article
title: Sufficiency for Gaussian hypergeometric functions to be uniformly convex
zbMATH Open document ID: 0951.30009
DOI: 10.1155/S0161171299227652
author: Saminathan Ponnusamy
author: Yong Chan Kim
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2000-12-26T00:00:00Z
full work available at URL: https://eudml.org/doc/48581
review text: The authors consider subclasses of the class \(A\) of functions holomorphic in the unit disk \(D\) and normalized by \(f(0)=f'(0)-1=0\), among them the class of uniformly convex functions, \(UCV\), and the classes \[ R_\eta (\beta)= \{f\in A\mid \min\text{Re}(e^{i\eta} \bigl(f'(z)-\beta)\bigr)> 0\quad \text{for}\quad z\in D\}. \] For the classical hypergeometric function \(F(a,b,c;z)\) they find conditions which imply that \(zF(a,b;c;z)\) belongs to one of the above classes. Further they derive conditions under which \(f\in R_\eta(\beta)\) implies \(zF(a,b,c;z)* f(z)\in UCV\), where * denotes the Hadamard products.
reviewed by: Karl-Joachim Wirths
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 33C20
zbMATH DE Number: 1417975
zbMATH Keywords: uniformly convex functions
zbMATH Keywords: Hadamard products
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1417975