New Subclasses of Analytic Functions with Respect to Symmetric and Conjugate Points

Huo Tang,Guan-Tie Deng

doi:10.1155/2013/578036

Abstract

We introduce new subclasses of close-to-convex and quasiconvex functions with respect to symmetric and conjugate points. The coefficient estimates for functions belonging to these classes are obtained.

Highlights

Let UU be the class of functions which are analytic and univalent in the open unit disk EE E EEE E EEEE E EE given by ∞ωω = 󵠈󵠈cckkzzkk (1)kkkk and satisfying the conditions ωωωωωω ωω ωωωωωωωω ω ωω ωω ω ωω
We introduce new subclasses of close-to-convex and quasiconvex functions with respect to symmetric and conjugate points. e coefficient estimates for functions belonging to these classes are obtained
Let UU be the class of functions which are analytic and univalent in the open unit disk EE E EEE E EEEE E EE given by ωω = 󵠈󵠈cckkzzkk kkkk and satisfying the conditions ωωωωωω ωω ωωωωωωωω ω ωω ωω ω ωω

Summary

Introduction

We introduce new subclasses of close-to-convex and quasiconvex functions with respect to symmetric and conjugate points. E coefficient estimates for functions belonging to these classes are obtained. Let SS∗ss be the subclass of functions fffffffff and satisfying the condition ff zzzz′ (zz) − Let SS∗cc be the subclass of functions fffffffff and satisfying the condition En, Das and Singh [6] introduced another class CCss, namely, convex functions with respect to symmetric points and satisfying the condition

Results

Conclusion