Properties of Functions Formed Using the Sakaguchi and Gao-Zhou Concept

Abstract

This paper introduces a new class related to close-to-convex functions denoted by K s k , N . This class is based on combining the concepts of starlike functions with respect to N-ply symmetry points of the order α , introduced by Chand and Singh; and K s ( k ) , introduced by Wang, Gao, and Yuan, which are generalizations of the classes of functions introduced by Sakaguchi and Gao and Zhou, respectively. We investigate the class for several properties including coefficient estimates, distortion and growth theorems, and the radius of convexity.

Keywords

• close-to-convex
• starlike with respect to n-ply symmetric points
• univalent