Title

Coefficients of univalent harmonic mappings

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

This document is currently not available here.

Share

COinS