On α -convex functions of order β with m -fold symmetry

Wancang Ma

International Journal of Mathematics and Mathematical Sciences, 1990, vol. 13, 1-7

Abstract:

This note is a continuation of the previous work [1,2,3]. First we get a new subordination for α -convex functions of order β when α = 1 − 2 β , which implies the rotation theorem for ( 1 − 2 β ) / m -convex functions of order β with m -fold symmetry. Then we extend the known results on α -convex functions of order β to the functions with m -fold symmetry. In particular, we give the sharp order of convexity of α -convex functions of order β with m -fold symmetry for α ≥ 1 , which is analogous in sharpness to a result given by Miller, Mocanu and Reade [1].

Date: 1990
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:635016

DOI: 10.1155/S0161171290000424

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