The Fekete-Szeg? Problem for a Subclass of Close-to-convex Functions of Order β Type γ with Respect to Symmetric Points

摘要

Let K_s(α,β,γ) be the class of normalized analytic function f that satisfy the condition Re{(2αz~2f"(z))/(h(z) - h(-z))+(2zf' (z))/(h(z)-h(-z))} > β where h is normalized starlike functions with respect to (w.r.t) symmetric points in the open unit disk D = {z : |z| < 1} for some 0 ≤ α < 1, 0 ≤ β < 1, 0 ≤ γ < 1. Sharp upper bounds for |a_n|, n = 2,3 and the Fekete-Szeg? inequalities are considered for this class of functions.