A Subclass of Quasi-Convex Functions with Respect to Symmetric Points

Abstract

Let Cs(A, B) denote the class of functions f which are analytic in an open unit disc D = {z: z < 1} and satisfying the condition 2(zf′(z))′/(f(z)-f(-z))′ ≺ 1+Az/1+Bz, -1 ≤ B < A ≤ 1, z ∈ D. In this paper, we consider the class Ks* (A, B) consisting of analytic functions f and satisfying (zf′(z))′/(g(z)-g(-z))′ ≺ 1+Az/1+Bz, g ∈ Cs(A,B), -1 ≤ B < A ≤ 1, z ∈ D. The aims of paper are to determine coefficient estimates, distortion bounds and preserving property for a certain integral operator for the class Ks* (A, B).