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Problemy Analiza — Issues of Analysis, 2019, Volume 8(26), Issue 2, Pages 37–50
DOI: https://doi.org/10.15393/j3.art.2019.6190 (Mi pa262) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Harmonic mappings onto $R$-convex domains

S. Yu. Grafab

a Petrozavodsk State University, 33, Lenina pr., Petrozavodsk, Russia
b Tver State University, 33, Zheliabova str., Tver, Russia
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DOI: https://doi.org/10.15393/j3.art.2019.6190
Abstract: The plane domain $D$ is called $R$-convex if $D$ contains each compact set bounded by two shortest sub-arcs of the radius $R$ with endpoints $w_1,\,w_2\in D$, $|w_1-w_2|\le 2R$. In this paper, we prove the conditions of $R$-convexity for images of disks under harmonic sense preserving functions. The coefficient bounds for harmonic mappings of the unit disk onto $R$-convex domains are obtained.
Keywords: harmonic mappings, R-convex domains, coefficient bounds.
Funding agency Grant number
Russian Science Foundation 17-11-01229
This work was supported by the Russian Science Foundation, project 17-11-01229.
Received: 22.04.2019
Revised: 06.06.2019
Accepted: 06.06.2019
Bibliographic databases:
Document Type: Article
UDC: 517.54
MSC: 30C45, 30C50, 30C55, 30C99
Language: English
Citation: S. Yu. Graf, “Harmonic mappings onto $R$-convex domains”, Probl. Anal. Issues Anal., 8(26):2 (2019), 37–50
Citation in format AMSBIB
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\by S.~Yu.~Graf
\paper Harmonic mappings onto $R$-convex domains
\jour Probl. Anal. Issues Anal.
\yr 2019
\vol 8(26)
\issue 2
\pages 37--50
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