Geodesic
Harmonic mappings with the fixed analytic part
Problemy analiza, Tome 10 (2021) no. 1, pp. 69-86

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In this article, we consider a class of sense-preserving harmonic mappings whose analytic part is convex in one direction. We prove that functions in this class are close-to-convex for certain values of parameters. Further, we obtain bounds on pre-Schwarzian derivatives and bounds on the Bloch's constant. Finally, we obtain coefficient bounds, growth and distortion results.
Keywords: univalent harmonic mappings, functions convex in one direction, pre-Schwarzian derivative, coefficient bound, growth and distortion results.
Mots-clés : Bloch's constant 
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     author = {Rajbala and Jugal K. Prajapat},
     title = {Harmonic mappings with the fixed analytic part},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2021_10_1_a4/}
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Rajbala; Jugal K. Prajapat. Harmonic mappings with the fixed analytic part. Problemy analiza, Tome 10 (2021) no. 1, pp. 69-86. http://geodesic.mathdoc.fr/item/PA_2021_10_1_a4/