INJECTIVITY OF SECTIONS OF CLOSE-TO-CONVEX HARMONIC MAPPINGS WITH FUNCTIONS CONVEX IN ONE DIRECTION AS ANALYTIC PART
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 the...
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| Format: | Article |
| Language: | English |
| Published: |
Petrozavodsk State University
2018-12-01
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| Series: | Проблемы анализа |
| Subjects: | |
| Online Access: | http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=5830&lang=ru |
| Summary: | 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. |
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| ISSN: | 2306-3424 2306-3432 |