Harmonic close-to-convex mappings
type: Item
instance of: scholarly article
title: Harmonic close-to-convex mappings
zbMATH Open document ID: 0999.30010
DOI: 10.1155/S1048953302000023
author: Jay M. Jahangiri
author: H. Silverman
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 2002-08-08T00:00:00Z
full work available at URL: https://eudml.org/doc/49556
review text: Let \(S_H\) denote the class of functions \(f= h+\overline g\) that are harmonic univalent in the unit disc \(\Delta= \{z:|z|< 1\}\) for which \(h\) and \(g\) have the forms \[ h(z)= z+\sum^\infty_{n=2} a_n z^n;\quad g(z)= \sum^\infty_{n=1} b_n z^n. \] In this paper the authors give some sufficient conditions for functions in \(S_H\) to be close-to-convex harmonic, or convex harmonic in \(\Delta\). Some convolution properties for harmonic functions are also investigated. For example it is proved: Theorem. If \(f= h+\overline g\) and \(\sum^\infty_{n=2} n|a_n|+ \sum^\infty_{n=1} n|b_n|\leq 1\), then \(f\) is convex harmonic in \(\Delta\).
reviewed by: Jan Stankiewicz
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 1777330
zbMATH Keywords: harmonic mappings
zbMATH Keywords: convex
zbMATH Keywords: close-to-convex
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1777330