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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
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.
Received: 22.04.2019 Revised: 06.06.2019 Accepted: 06.06.2019
Citation:
S. Yu. Graf, “Harmonic mappings onto $R$-convex domains”, Probl. Anal. Issues Anal., 8(26):2 (2019), 37–50
Linking options:
https://www.mathnet.ru/eng/pa262 https://www.mathnet.ru/eng/pa/v26/i2/p37
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Abstract page: | 191 | Full-text PDF : | 52 | References: | 20 |
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