SOME PROPERTIES OF HARMONIC UNIVALENT FUNCTIONS IN TERMS OF RUSCHEWEYH DERIVATIVES

Waggas Galib Atshan (India) and S. R. Kulkarni (India)

Received June 16, 2007; Revised August 11, 2007

Abstract

We define a class of harmonic univalent functions defined by Ruscheweyh derivatives of the form  and study some properties of this class, e.g., necessary and sufficient coefficient conditions, extreme points, convex combination, convolution and integral operator.

Keywords and phrases: harmonic functions, Ruscheweyh derivative, extreme points, convex combination, convolution and integral operator.