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JMB Journal of Microbiolog and Biotechnology

OPEN ACCESS eISSN 0454-8124
pISSN 1225-6951
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Original Article

Kyungpook Mathematical Journal 2009; 49(4): 751-761

Published online December 23, 2009

Copyright © Kyungpook Mathematical Journal.

Some Properties of Harmonic Functions Defined by Convolution

Kaushal Kishor Dixit, Saurabh Porwal

Department of Mathematics, Janta College, Bakewar, Etawah-206124 $($U.P.$)$ India

Abstract

In this paper, we introduce and study a comprehensive family of harmonic univalent functions which contains various well-known classes of harmonic univalent functions as well as many new ones. Also, we improve some results obtained by Frasin cite{key-3} and obtain coefficient bounds, distortion bounds and extreme points, convolution conditions and convex combination are also determined for functions in this family. It is worth mentioning that many of our results are either extensions or new approaches to those corresponding previously known results.

Keywords: harmonic, analytic and univalent functions