Sharp Estimates of Logarithmic Coefficients for a Certain Class of Starlike Functions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911520758169600 |
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| author | Ahamed, Molla Basir Mandal, Sanju |
| author_facet | Ahamed, Molla Basir Mandal, Sanju |
| contents | In this article, we investigate the extremal properties of logarithmic coefficients for the class $\mathcal{S}_{ch}^*$ of starlike functions associated with the hyperbolic cosine function. We establish the sharp upper bounds for the initial logarithmic coefficients $γ_n$ for $n=1, 2, 3$, and determine the precise bound for the second Hankel determinant $H_{2,1}(F_f/2)$ within this class. Furthermore, we extend our analysis to the inverse functions, deriving sharp estimates for the logarithmic inverse coefficients and the corresponding second Hankel determinant $|H_{2,1}(F_{f^{-1}}/2)|$. Additionally, we provide sharp bounds for the moduli differences of both logarithmic and inverse logarithmic coefficients. The sharpness of all obtained inequalities is verified through the construction of specific extremal functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_15659 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp Estimates of Logarithmic Coefficients for a Certain Class of Starlike Functions Ahamed, Molla Basir Mandal, Sanju Complex Variables Primary 30C45, Secondary 30C50, 30C80 In this article, we investigate the extremal properties of logarithmic coefficients for the class $\mathcal{S}_{ch}^*$ of starlike functions associated with the hyperbolic cosine function. We establish the sharp upper bounds for the initial logarithmic coefficients $γ_n$ for $n=1, 2, 3$, and determine the precise bound for the second Hankel determinant $H_{2,1}(F_f/2)$ within this class. Furthermore, we extend our analysis to the inverse functions, deriving sharp estimates for the logarithmic inverse coefficients and the corresponding second Hankel determinant $|H_{2,1}(F_{f^{-1}}/2)|$. Additionally, we provide sharp bounds for the moduli differences of both logarithmic and inverse logarithmic coefficients. The sharpness of all obtained inequalities is verified through the construction of specific extremal functions. |
| title | Sharp Estimates of Logarithmic Coefficients for a Certain Class of Starlike Functions |
| topic | Complex Variables Primary 30C45, Secondary 30C50, 30C80 |
| url | https://arxiv.org/abs/2603.15659 |