CONVOLUTIONS OF A SUBCLASS OF HARMONIC UNIVALENT MAPPINGS


YAŞAR E., Ozdemir O.

TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, vol.10, no.2, pp.353-359, 2020 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 2
  • Publication Date: 2020
  • Journal Name: TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index, Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.353-359
  • Keywords: Harmonic mappings, harmonic convolution, univalence, CONVEX

Abstract

The main object of this paper is to investigate the convolution of a subclass of harmonic univalent mappings which is denoted by f(a) and generalized harmonic univalent mapping which is denoted by P-c. We obtained P-c * f(a) 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.