Sections of univalent harmonic mappings

Authors

Saminathan Ponnusamy, Indian Statistical Institute Chennai
Anbareeswaran Sairam Kaliraj, Indian Statistical Institute Chennai
Victor V. Starkov, PetrSU

Article Type

Research Article

Publication Title

Indagationes Mathematicae

Abstract

In this article, we determine the radius of univalence of sections of normalized univalent harmonic mappings for which the range is convex (resp. starlike, close-to-convex, convex in one direction). Our result on the radius of univalence of section sn,n(f) is sharp especially when the corresponding mappings have convex range. In this case, each section sn,n(f) is univalent in the disk of radius 1/4 for all n≥2, which may be compared with classical result of Szegö on conformal mappings.

First Page

527

Last Page

540

DOI

10.1016/j.indag.2017.01.001

Publication Date

4-1-2017

Comments

Open Access, Bronze, Green

Recommended Citation

Ponnusamy, Saminathan; Kaliraj, Anbareeswaran Sairam; and Starkov, Victor V., "Sections of univalent harmonic mappings" (2017). Journal Articles. 2623.
https://digitalcommons.isical.ac.in/journal-articles/2623