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Probl. Anal. Issues Anal., 2019, Volume 8(26), Issue 2, Pages 37–50 (Mi pa262)  

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

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.


DOI: https://doi.org/10.15393/j3.art.2019.6190

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Bibliographic databases:

UDC: 517.54
MSC: 30C45, 30C50, 30C55, 30C99
Received: 22.04.2019
Revised: 06.06.2019
Accepted:06.06.2019
Language:

Citation: S. Yu. Graf, “Harmonic mappings onto $R$-convex domains”, Probl. Anal. Issues Anal., 8(26):2 (2019), 37–50

Citation in format AMSBIB
\Bibitem{Gra19}
\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
\mathnet{http://mi.mathnet.ru/pa262}
\crossref{https://doi.org/10.15393/j3.art.2019.6190}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000471801400003}


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