CONVOLUTIONS OF A SUBCLASS OF HARMONIC UNIVALENT MAPPINGS

CONVOLUTIONS OF A SUBCLASS OF HARMONIC UNIVALENT MAPPINGS

E. Yaşar, Ö. Özdemir

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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(1a) 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.