International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 4, Pages 765-773
doi:10.1155/S0161171299227652
Sufficiency for Gaussian hypergeometric functions to be uniformly convex
Yong Chan Kim1
and S. Ponnusamy2
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
Abstract
Let F(a,b;c;z) be the classical hypergeometric function and f be a normalized analytic functions defined on the unit disk 𝒰. Let an operator Ia,b;c(f) be defined by [Ia,b;c(f)](z)=zF(a,b;c;z)*f(z). In this paper the authors identify two subfamilies of analytic functions ℱ1 and ℱ2 and obtain conditions on the parameters a,b,c such that f∈ℱ1 implies Ia,b;c(f)∈ℱ2.