HARMONIC MAPPINGS WITH THE FIXED ANALYTIC PART
In this article, we consider a class of sense-preserving harmonic mappings whose analytic part is convex in one direction. We prove that functions in this class are close-to-convex for certain values of parameters. Further, we obtain bounds on preSchwarzian derivatives and bounds on the Bloch’s...
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| Format: | Article |
| Language: | English |
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Petrozavodsk State University
2021-02-01
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| Series: | Проблемы анализа |
| Subjects: | |
| Online Access: | https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=8850&lang=ru |
| _version_ | 1818677134620622848 |
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| author | Rajbala, Jugal K. Prajapat |
| author_facet | Rajbala, Jugal K. Prajapat |
| author_sort | Rajbala, Jugal K. Prajapat |
| collection | DOAJ |
| description | In this article, we consider a class of sense-preserving
harmonic mappings whose analytic part is convex in one
direction. We prove that functions in this class are close-to-convex
for certain values of parameters. Further, we obtain bounds on preSchwarzian derivatives and bounds on the Bloch’s
constant. Finally, we obtain coefficient bounds, growth and
distortion results. |
| first_indexed | 2024-12-17T08:54:33Z |
| format | Article |
| id | doaj.art-25417478b347427e81591924182f99ae |
| institution | Directory Open Access Journal |
| issn | 2306-3424 2306-3432 |
| language | English |
| last_indexed | 2024-12-17T08:54:33Z |
| publishDate | 2021-02-01 |
| publisher | Petrozavodsk State University |
| record_format | Article |
| series | Проблемы анализа |
| spelling | doaj.art-25417478b347427e81591924182f99ae2022-12-21T21:55:59ZengPetrozavodsk State UniversityПроблемы анализа2306-34242306-34322021-02-0110 (28)1698610.15393/j3.art.2021.8850HARMONIC MAPPINGS WITH THE FIXED ANALYTIC PARTRajbala, Jugal K. Prajapat0Department of Mathematics, Central University of RajasthanIn this article, we consider a class of sense-preserving harmonic mappings whose analytic part is convex in one direction. We prove that functions in this class are close-to-convex for certain values of parameters. Further, we obtain bounds on preSchwarzian derivatives and bounds on the Bloch’s constant. Finally, we obtain coefficient bounds, growth and distortion results.https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=8850&lang=ruunivalent harmonic mappingsfunctions convex in one directionpre-schwarzian derivativebloch’s constantcoefficient boundgrowth and distortion results |
| spellingShingle | Rajbala, Jugal K. Prajapat HARMONIC MAPPINGS WITH THE FIXED ANALYTIC PART Проблемы анализа univalent harmonic mappings functions convex in one direction pre-schwarzian derivative bloch’s constant coefficient bound growth and distortion results |
| title | HARMONIC MAPPINGS WITH THE FIXED ANALYTIC PART |
| title_full | HARMONIC MAPPINGS WITH THE FIXED ANALYTIC PART |
| title_fullStr | HARMONIC MAPPINGS WITH THE FIXED ANALYTIC PART |
| title_full_unstemmed | HARMONIC MAPPINGS WITH THE FIXED ANALYTIC PART |
| title_short | HARMONIC MAPPINGS WITH THE FIXED ANALYTIC PART |
| title_sort | harmonic mappings with the fixed analytic part |
| topic | univalent harmonic mappings functions convex in one direction pre-schwarzian derivative bloch’s constant coefficient bound growth and distortion results |
| url | https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=8850&lang=ru |
| work_keys_str_mv | AT rajbalajugalkprajapat harmonicmappingswiththefixedanalyticpart |