International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 2, Pages 287-293
On -convex functions of order with -fold symmetry
Department of Mathematics, Northwest University, Xian, China
Received 23 July 1987; Revised 22 September 1987
Copyright © 1990 Wancang Ma. 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.
This note is a continuation of the previous work [1,2,3]. First we get a new subordination for -convex functions of order when , which implies the rotation theorem for -convex functions of order with -fold symmetry. Then we extend the known results on -convex functions of order to the functions with -fold symmetry. In particular, we give the sharp order of convexity of -convex functions of order with -fold symmetry for , which is analogous in sharpness to a result given by Miller, Mocanu and Reade .