|
This article is cited in 1 scientific paper (total in 1 paper)
Injectivity of sections of close-to-convex harmonic mappings with functions convex in one direction as analytic part
A. Sairam Kaliraj Indian Institute of Technology Ropar,
Nangal Road, Rupnagar, Punjab, 140001, India
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.
Received: 24.02.2018 Revised: 28.11.2018 Accepted: 28.11.2018
Citation:
A. Sairam Kaliraj, “Injectivity of sections of close-to-convex harmonic mappings with functions convex in one direction as analytic part”, Probl. Anal. Issues Anal., 7(25):2 (2018), 131–143
Linking options:
https://www.mathnet.ru/eng/pa252 https://www.mathnet.ru/eng/pa/v25/i2/p131
|
Statistics & downloads: |
Abstract page: | 135 | Full-text PDF : | 50 | References: | 13 |
|