Logarithmic coefficients of close-to-convex functions
| Autor: | Ali, Md Firoz, Thomas, D. K., Vasudevarao, A. |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| Popis: | For an analytic and univalent function $f$ in the unit disk $\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}$ with the normalization $f(0)=0=f'(0)-1$, the logarithmic coefficients $\gamma_n$ are defined by $\log \frac{f(z)}{z}= 2\sum_{n=1}^{\infty} \gamma_n z^n$. In the present paper, we consider the class of close-to-convex functions (with argument $0$), and determine the sharp upper bound of $|\gamma_3|$ for such functions $f$, which proves a recent conjecture of the first and third authors [1]. Comment: This paper has been withdrawn by the author due to a error in the proof |
| Databáze: | arXiv |
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