Sufficiency for Gaussian hypergeometric functions to be uniformly convexReport as inadecuate

Sufficiency for Gaussian hypergeometric functions to be uniformly convex - Download this document for free, or read online. Document in PDF available to download.

International Journal of Mathematics and Mathematical Sciences - Volume 22 1999, Issue 4, Pages 765-773

Department of Mathematics, Yeungnam University, 214-1, Daedong, Gyongsan 712-749, Korea

Department 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 Hindawi Publishing Corporation. 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.


Let Fa,b;c;z be the classical hypergeometric function and f be a normalized analytic functions defined on the unit disk ūĚíį. Let an operator Ia,b;cf be defined by Ia,b;cfz=zFa,b;c;z*fz. In this paper the authors identify two subfamilies of analytic functions‚ĄĪ1 and ‚ĄĪ2 and obtain conditions on the parameters a,b,c such that f‚ąą‚ĄĪ1 implies Ia,b;cf‚ąą‚ĄĪ2.

Author: Yong Chan Kim and S. Ponnusamy



Related documents