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

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Yaşar E., Yalçın Tokgöz S.

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

  • Publication Type: Article / Article
  • Volume: 45 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.3906/mat-2004-50
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.678-694
  • Keywords: Harmonic, univalent, close-to-convex, hypergeometric function
  • Bursa Uludag University Affiliated: Yes

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.