Author:
Beig Subzar,Sim Young Jae,Cho Nak Eun
Abstract
AbstractLet $\psi_{\mu,\nu}(z)=(1-2\cos\nu e^{i\mu}z+e^{2i\mu}z^{2})^{-1}$ψμ,ν(z)=(1−2cosνeiμz+e2iμz2)−1, $\mu,\nu\in[0,2\pi)$μ,ν∈[0,2π) and p be an analytic mapping with $\operatorname{Re} p>0$Rep>0 on the open unit disk. We consider the sense-preserving planar harmonic mappings $f=h+\overline{g}$f=h+g‾, which are shears of the mapping $\int_{0}^{z} \psi_{\mu,\nu}(\xi) p(\xi)\,{d}\xi$∫0zψμ,ν(ξ)p(ξ)dξ in the direction μ. These mappings include the harmonic right half-plan mappings, vertical strip mappings, and their rotations. For various choices of dilatations $g'/h'$g′/h′ of f, sufficient conditions are found for the convex combinations of these mappings to be univalent and convex in the direction μ.
Funder
National Research Foundation of Korea
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Cited by
4 articles.
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