SHARP BOUNDS FOR THE SECOND HANKEL DETERMINANT OF LOGARITHMIC COEFFICIENTS FOR PARABOLIC STARLIKE AND UNIFORMLY CONVEX FUNCTIONS OF ORDER α

BULUT S.

Khayyam Journal of Mathematics, cilt.10, sa.1, ss.51-69, 2024 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 10 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.22034/kjm.2023.395878.2856
  • Dergi Adı: Khayyam Journal of Mathematics
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.51-69
  • Anahtar Kelimeler: Analytic function, logarithmic coefficients, parabolic-starlike functions, sub-ordination, univalent function
  • Kocaeli Üniversitesi Adresli: Evet

Özet

Let A denote the class of analytic functions f in the open unit disk U normalized by f(0) = f′ (0) − 1 = 0, and let S be the class of all functions f ∈ A that are univalent in U. For a function f ∈ S, the logarithmic coefficients δn (n = 1, 2, 3, …) are defined by (Formula Presented) For 0 ≤ α < 1, let Sp (α) and UCV (α) denote the classes of functions f ∈ A such that (Formula Presented) and (Formula Presented) respectively. In the present paper, we determine the sharp upper bound for |δn | (n = 1, 2, 3, …) of functions f belonging to the classes Sp (α). Also, we obtain upper bounds for |δn | (n = 1, 2, 3) of functions belonging to the class UCV (α).