New subclass of the class of close-to-convex harmonic mappings defined by a third-order differential inequality

Çakmak S., Yaşar E., Yalçın Tokgöz S.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.51, no.1, pp.172-186, 2022 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.15672/hujms.922981
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), TR DİZİN (ULAKBİM)
  • Page Numbers: pp.172-186
  • Keywords: harmonic, univalent, close-to-convex, coefficient estimates, convolution, STARLIKE
  • Bursa Uludag University Affiliated: Yes

Abstract

In this paper, we introduce a new subclass of harmonic functions f = s + t in the open [ ) Re gamma s '(z) + delta zs ''(z) + (5-7 (5-7 z2s ''' (z) - lambda gamma t '(z) + delta zt ''(z) + z2t ''' (z) , 2 2 where 0 <= lambda < gamma <= delta, z is an element of U. We determine several properties of this class such as close-toconvexity, coefficient bounds, and growth estimates. We also prove that this class is closed under convex combination and convolution of its members. Furthermore, we investigate the properties of fully starlikeness and fully convexity of the class.