Neighbourhoods of two new classes of harmonic univalent functions with varying arguments

Yaşar E., Yalcin S.

Mathematica Slovaca, vol.64, no.6, pp.1409-1420, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 64 Issue: 6
  • Publication Date: 2014
  • Doi Number: 10.2478/s12175-014-0283-x
  • Journal Name: Mathematica Slovaca
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1409-1420
  • Keywords: harmonic, k-starlike, k-uniformly convex, hypergeometric functions, varying arguments, convolution, neighbourhood, HYPERGEOMETRIC-FUNCTIONS, STARLIKE, OPERATORS
  • Bursa Uludag University Affiliated: Yes

Abstract

© 2014, Versita Warsaw and Springer-Verlag Wien.In this paper, two new classes of harmonic univalent functions with varying arguments are defined by using planar harmonic convolution operator involving hypergeometric functions. Those classes are of special interest because they contain various classes of well-known harmonic univalent functions such as the classes of k-starlike and k-uniformly convex harmonic univalent functions. The main purpose of this paper is to investigate neighbourhoods of the classes in question.