INJECTIVITY OF SECTIONS OF CLOSE-TO-CONVEX HARMONIC MAPPINGS WITH FUNCTIONS CONVEX IN ONE DIRECTION AS ANALYTIC PART
Journal Title: Проблемы анализа-Issues of Analysis - Year 2018, Vol 7, Issue 2
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.
Authors and Affiliations
A. S. Kaliraj
Keywords
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- EP ID EP437249
- DOI 10.15393/j3.art.2018.5830
- Views 70
- Downloads 0
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