Coefficients 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

Monatshefte fur Mathematik

Abstract

Let SH0 denote the class of all functions f(z)=h(z)+g(z)¯=z+∑n=2∞anzn+∑n=2∞bnzn¯ that are sense-preserving, harmonic and univalent in the open unit disk | z| < 1. The coefficient conjecture for SH0 is still open even for | a2|. The aim of this paper is to show that if f=h+g¯∈SH0 then | an| < 5.24 × 10 - 6n17 and | bn| < 2.32 × 10 - 7n17 for all n≥ 3. Making use of these coefficient estimates, we also obtain radius of univalence of sections of univalent harmonic mappings.

First Page

453

Last Page

470

DOI

10.1007/s00605-017-1038-x

Publication Date

7-1-2018

Comments

All Open Access, Green

Recommended Citation

Ponnusamy, Saminathan; Kaliraj, Anbareeswaran Sairam; and Starkov, Victor V., "Coefficients of univalent harmonic mappings" (2018). Journal Articles. 1337.
https://digitalcommons.isical.ac.in/journal-articles/1337