On -convex functions of order with -fold symmetry
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 .
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