Open Access

On Harmonic Functions Defined by Derivative Operator

Journal of Inequalities and Applications20072008:263413

https://doi.org/10.1155/2008/263413

Received: 16 September 2007

Accepted: 26 November 2007

Published: 3 December 2007

Abstract

Let denote the class of functions that are harmonic univalent and sense-preserv- ing in the unit disk , where . In this paper, we introduce the class of functions which are harmonic in . A sufficient coefficient of this class is determined. It is shown that this coefficient bound is also necessary for the class if , where and . Coefficient conditions, such as distortion bounds, convolution conditions, convex combination, extreme points, and neighborhood for the class , are obtained.

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Authors’ Affiliations

(1)
School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia

Copyright

© K. Al-Shaqsi and M. Darus. 2008

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.