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

Çakmak S., YAŞAR E., YALÇIN TOKGÖZ S.

Hacettepe Journal of Mathematics and Statistics, cilt.51, sa.1, ss.172-186, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 51 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.15672/hujms.922981
  • Dergi Adı: Hacettepe Journal of Mathematics and Statistics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.172-186
  • Anahtar Kelimeler: harmonic, univalent, close-to-convex, coefficient estimates, convolution
  • İstanbul Gelişim Üniversitesi Adresli: Hayır

Özet

In this paper, we introduce a new subclass of harmonic functions f = s + t in the open unit[ disk U = {z ∈ ℂ: (|z| <)1} satisfying ] Re (formula presented) where 0 ≤ λ < γ ≤ δ, z ∈ U. We determine several properties of this class such as close-to-convexity, 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.