Geodesic
Harmonic mappings onto $R$-convex domains
Problemy analiza, Tome 8 (2019) no. 2, pp. 37-50

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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, coefficient bounds.
Mots-clés : R-convex domains 
@article{PA_2019_8_2_a2,
     author = {S. Yu. Graf},
     title = {Harmonic mappings onto $R$-convex domains},
     journal = {Problemy analiza},
     pages = {37--50},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2019_8_2_a2/}
}
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S. Yu. Graf. Harmonic mappings onto $R$-convex domains. Problemy analiza, Tome 8 (2019) no. 2, pp. 37-50. http://geodesic.mathdoc.fr/item/PA_2019_8_2_a2/