Results on Logarithmic Coefficients for the Class of Bounded Turning Functions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913678621671424 |
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| author | Mandal, Sanju Ahamed, Molla Basir |
| author_facet | Mandal, Sanju Ahamed, Molla Basir |
| contents | It is crucial to explore the sharp bounds of logarithmic coefficients and the Hankel determinant involving logarithmic coefficients as part of coefficient problems in various function classes. Our primary objective in this study is to determine the sharp bounds for logarithmic coefficients as well as logarithmic inverse coefficients of bounded analytic functions associated with a bean-shaped domain in the class $\mathcal{BT_\mathfrak{B}}$. For this class, we also establish the sharp bounds for the second Hankel determinant involving logarithmic coefficients as well as logarithmic inverse coefficients. In addition, we establish sharp bounds for the generalized Zalcman conjecture inequality and the moduli differences of logarithmic coefficients for the class $\mathcal{BT_\mathfrak{B}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02898 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Results on Logarithmic Coefficients for the Class of Bounded Turning Functions Mandal, Sanju Ahamed, Molla Basir Complex Variables Primary 30C45, Secondary 30C50, 30C55 It is crucial to explore the sharp bounds of logarithmic coefficients and the Hankel determinant involving logarithmic coefficients as part of coefficient problems in various function classes. Our primary objective in this study is to determine the sharp bounds for logarithmic coefficients as well as logarithmic inverse coefficients of bounded analytic functions associated with a bean-shaped domain in the class $\mathcal{BT_\mathfrak{B}}$. For this class, we also establish the sharp bounds for the second Hankel determinant involving logarithmic coefficients as well as logarithmic inverse coefficients. In addition, we establish sharp bounds for the generalized Zalcman conjecture inequality and the moduli differences of logarithmic coefficients for the class $\mathcal{BT_\mathfrak{B}}$. |
| title | Results on Logarithmic Coefficients for the Class of Bounded Turning Functions |
| topic | Complex Variables Primary 30C45, Secondary 30C50, 30C55 |
| url | https://arxiv.org/abs/2502.02898 |