Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality


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YAŞAR E. , YALÇIN TOKGÖZ S.

TURKISH JOURNAL OF MATHEMATICS, vol.45, no.2, pp.678-694, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.3906/mat-2004-50
  • Title of Journal : TURKISH JOURNAL OF MATHEMATICS
  • Page Numbers: pp.678-694
  • Keywords: Harmonic, univalent, close-to-convex, hypergeometric function

Abstract

In this paper, we consider a class of normalized harmonic functions in the unit disk satisfying a third-order differential inequality and we investigate several properties of this class such as close-to-convexity, coefficient bounds, growth estimates, sufficient coefficient condition, and convolution. Moreover, as an application, we construct harmonic polynomials involving Gaussian hypergeometric function which belong to the considered class. We also provide examples illustrating graphically with the help of Maple.