Geodesic
Injectivity of sections of close-to-convex harmonic mappings with functions convex in one direction as analytic part
Problemy analiza, Tome 7 (2018) no. 2, pp. 131-143

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In this article, we prove a two-points distortion theorem and obtain sharp coefficient estimates for the families of close-to-convex harmonic mappings whose analytic part is a function convex in one direction. By making use of these results, we determine the radius of univalence of sections of these families in terms of zeros of a certain equation. the lower bound for the radius of univalence has been obtained explicitly for the case $\alpha = 1/2$. Comparison of radius of univalence of the sections has been shown by providing a table of numerical estimates for the special choices of $\alpha$.
Keywords: Univalent Harmonic, convex in one direction, close-to-convex, partial sums
Mots-clés : sections. 
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     author = {A. Sairam Kaliraj},
     title = {Injectivity of sections of close-to-convex harmonic mappings with functions convex in one direction as analytic part},
     journal = {Problemy analiza},
     pages = {131--143},
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     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2018_7_2_a8/}
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A. Sairam Kaliraj. Injectivity of sections of close-to-convex harmonic mappings with functions convex in one direction as analytic part. Problemy analiza, Tome 7 (2018) no. 2, pp. 131-143. http://geodesic.mathdoc.fr/item/PA_2018_7_2_a8/