International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 4, Pages 769-772

On α-convex functions of order β

Seiichi Fukui

Department of Mathematics, Faculty of Education, Wakayama University, Japan

Received 1 November 1995

Copyright © 1997 Seiichi Fukui. 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.


In 1969 Mocanu [1] introduced and studied a new class of analytic functions consisting of α-convex functions. Many mathematicians have studied and shown the properties of this class. Now we will define new classes like that Mocanu class and then investigate and give some results. The class of α-convex functions of order β partially includes Mocanu's class.