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The Second Hankel Determinant of Logarithmic Coefficients for Strongly Ozaki Close-to-Convex Functions

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Abstract

The aim of this paper is to determine sharp bound for the second Hankel determinant of logarithmic coefficients \(H_{2,1}(F_{f}/2)\) of strongly Ozaki close-to-convex functions in the open unit disk. Furthermore, sharp bound of \(H_{2,1}(F_{f^{-1}}/2)\), where \(f^{-1}\) is the inverse function of f, is also computed. The results show an invariance property of the second Hankel determinants of logarithmic coefficients \(H_{2,1}(F_{f}/2)\) and \(H_{2,1}(F_{f^{-1}}/2)\) for strongly convex functions.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Dicle University, Diyarbakır, Türkiye

    Sevtap Sümer Eker, Bilal Çekiç & Bilal Şeker

  2. Department of Complex Analysis, Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, ul. Słoneczna 54, 10-710, Olsztyn, Poland

    Adam Lecko

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  1. Sevtap Sümer Eker
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  4. Bilal Şeker
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All authors contributed equally to the planning, execution, and analysis of this research paper.

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Communicated by Rosihan M. Ali.

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Sümer Eker, S., Lecko, A., Çekiç, B. et al. The Second Hankel Determinant of Logarithmic Coefficients for Strongly Ozaki Close-to-Convex Functions. Bull. Malays. Math. Sci. Soc. 46, 183 (2023). https://doi.org/10.1007/s40840-023-01580-5

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  • DOI: https://doi.org/10.1007/s40840-023-01580-5

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