CONVOLUTIONS OF A SUBCLASS OF HARMONIC UNIVALENT MAPPINGS

Abstract

The main object of this paper is to investigate the convolution of a subclass of harmonic univalent mappings which is denoted by fa and generalized harmonic univalent mapping which is denoted by Pc. We obtained Pc ∗ fa is univalent and convex in the horizantal direction for 0 < c ≤ 2 1−a 1+a . In addition, we present an example and illustrate it graphically with the help of Maple to explain the behaviour of image domain

Keywords

• Harmonic mappings,harmonic convolution,univalence

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