Abstract:
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, sections.
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