This article is cited in 1 paper

Harmonic mappings onto $R$-convex domains

S. Yu. Graf<sup>ab

a</sup> 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.

UDC: 517.54

MSC: 30C45, 30C50, 30C55, 30C99

Received: 22.04.2019
Revised: 06.06.2019
Accepted: 06.06.2019

Language: English

DOI: 10.15393/j3.art.2019.6190

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