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

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BULUT S.

Khayyam Journal of Mathematics, vol.10, no.1, pp.51-69, 2024 (Scopus)

• Publication Type: Article / Article
• Volume: 10 Issue: 1
• Publication Date: 2024
• Doi Number: 10.22034/kjm.2023.395878.2856
• Journal Name: Khayyam Journal of Mathematics
• Journal Indexes: Scopus
• Page Numbers: pp.51-69
• Keywords: Analytic function, logarithmic coefficients, parabolic-starlike functions, sub-ordination, univalent function
• Kocaeli University Affiliated: Yes

Abstract

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).