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
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