International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 3, Pages 455-467

Generalized classes of starlike and convex functions of order α

Shigeyoshi Owa1 and C. Y. Shen2

1Department of Mathematics, Kinki University, Higashi-Osaka, Osaka 577, Japan
2Department of Mathematics and Statistics, Simon Fraser University, Burnaby V5A 1S6, B.C., Canada

Received 1 June 1985

Copyright © 1985 Shigeyoshi Owa and C. Y. Shen. 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.


We have introduced, in this paper, the generalized classes of starlike and convex functions of order α by using the fractional calculus. We then proved some subordination theorems, argument theorems, and various results of modified Hadamard product for functions belonging to these classes. We have also established some properties about the generalized Libera operator defined on these classes of functions.