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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Petrozavodsk State University
2018-12-01
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| Series: | Проблемы анализа |
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| Online Access: | http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=5830&lang=ru |
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doaj-741fc6bf694f4d1a90ae180fc5c508e02021-07-02T07:14:09ZengPetrozavodsk State UniversityПроблемы анализа2306-34242306-34322018-12-017(25)213114310.15393/j3.art.2018.5830INJECTIVITY OF SECTIONS OF CLOSE-TO-CONVEX HARMONIC MAPPINGS WITH FUNCTIONS CONVEX IN ONE DIRECTION AS ANALYTIC PARTA. Sairam Kaliraj0Indian Institute of Technology RoparIn 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.http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=5830&lang=ruconvex in one directioncloseto-convexpartial sumssectionsбUnivalent Harmonicsections |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
A. Sairam Kaliraj |
| spellingShingle |
A. Sairam Kaliraj INJECTIVITY OF SECTIONS OF CLOSE-TO-CONVEX HARMONIC MAPPINGS WITH FUNCTIONS CONVEX IN ONE DIRECTION AS ANALYTIC PART Проблемы анализа convex in one direction closeto-convex partial sums sectionsб Univalent Harmonic sections |
| author_facet |
A. Sairam Kaliraj |
| author_sort |
A. Sairam Kaliraj |
| title |
INJECTIVITY OF SECTIONS OF CLOSE-TO-CONVEX HARMONIC MAPPINGS WITH FUNCTIONS CONVEX IN ONE DIRECTION AS ANALYTIC PART |
| title_short |
INJECTIVITY OF SECTIONS OF CLOSE-TO-CONVEX HARMONIC MAPPINGS WITH FUNCTIONS CONVEX IN ONE DIRECTION AS ANALYTIC PART |
| title_full |
INJECTIVITY OF SECTIONS OF CLOSE-TO-CONVEX HARMONIC MAPPINGS WITH FUNCTIONS CONVEX IN ONE DIRECTION AS ANALYTIC PART |
| title_fullStr |
INJECTIVITY OF SECTIONS OF CLOSE-TO-CONVEX HARMONIC MAPPINGS WITH FUNCTIONS CONVEX IN ONE DIRECTION AS ANALYTIC PART |
| title_full_unstemmed |
INJECTIVITY OF SECTIONS OF CLOSE-TO-CONVEX HARMONIC MAPPINGS WITH FUNCTIONS CONVEX IN ONE DIRECTION AS ANALYTIC PART |
| title_sort |
injectivity of sections of close-to-convex harmonic mappings with functions convex in one direction as analytic part |
| publisher |
Petrozavodsk State University |
| series |
Проблемы анализа |
| issn |
2306-3424 2306-3432 |
| publishDate |
2018-12-01 |
| description |
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. |
| topic |
convex in one direction closeto-convex partial sums sectionsб Univalent Harmonic sections |
| url |
http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=5830&lang=ru |
| work_keys_str_mv |
AT asairamkaliraj injectivityofsectionsofclosetoconvexharmonicmappingswithfunctionsconvexinonedirectionasanalyticpart |
| _version_ |
1721336374846554112 |