Injectivity of sections of close-to-convex harmonic mappings with functions convex in one direction as analytic part

Abstract

In this article, we prove a two-points distortion theorem and obtain sharp coefficient estimates for the families of close-toconvex harmonic mappings whose analytic part is a function convex in one direction. By making use of these results, we determine the radius of univalence of sections of these families in terms of zeros of a certain equation. the lower bound for the radius of univalence has been obtained explicitly for the case α = 1/2. Comparison of radius of univalence of the sections has been shown by providing a table of numerical estimates for the special choices of α.