International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 4, Pages 765-773
Sufficiency for Gaussian hypergeometric functions to be uniformly convex
1Department of Mathematics, Yeungnam University, 214-1, Daedong, Gyongsan 712-749, Korea
2Department of Mathematics, University of Helsinki, P. O. Box 4, Hallitskatu 15, Helsinki FIN-00014, Finland
Received 10 July 1997; Revised 27 October 1997
Copyright © 1999 Yong Chan Kim and S. Ponnusamy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
AbstractLet be the classical hypergeometric function and be a normalized analytic functions defined on the unit disk . Let an operator be defined by . In this paper the authors identify two subfamilies of analytic functions
and and obtain conditions on the parameters such that implies .