SOME RESULTS ASSOCIATED WITH THE ANALYTIC PART OF HARMONIC UNIVALENT FUNCTIONS

Abdul Rahman S. Juma (India), S. R. Kulkarni (India) and R. K. Raina (India)

Received July 19, 2007

Abstract

In this paper we introduce a new class  of harmonic univalent functions defined in the open unit disk. We derive the fundamental geometric properties like the coefficient bound inequality, distortion theorems and radii of starlikeness, close-to-convexity and convexity for the analytic part of the harmonic function belonging to the class  Applications of fractional calculus operators are exhibited in establishing the distortion theorems.

Keywords and phrases: harmonic functions, analytic and univalent functions, distortion theorems, fractional calculus operators, radii of starlike, close-to-convex and convex functions.