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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2018
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| Accès en ligne: | https://arxiv.org/abs/1811.01271 |
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| _version_ | 1866914263800479744 |
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| author | Kargar, R. Sokół, J. Mahzoon, H. |
| author_facet | Kargar, R. Sokół, J. Mahzoon, H. |
| contents | Let $\mathcal{S}^*(α_1,α_2)$, where $ α_1, α_2 \in (0,1]$, represent the class of functions $f$ that are analytic in the open unit disk $\mathbb{D}$, normalized by $f(0) = f'(0) - 1=0$, and satisfying the following double-sided inequality: \begin{equation*}
-\frac{πα_1}{2}< \arg\left\{\frac{zf'(z)}{f(z)}\right\} <\frac{πα_2}{2}, \quad (z\in\mathbb{D}). \end{equation*} In this manuscript, we estimate the coefficients and logarithmic coefficients associated with functions that belong to the class $\mathcal{S}^*(α_1,α_2)$. As a result, we provide a general bound for the coefficients of a strongly starlike function, which has been an open question until now. Finally, we derive upper and lower bounds for the expression ${\rm Re}\{zf'(z)/f(z)\}$, where $f\in \mathcal{S}^*(α_1,α_2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1811_01271 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On a certain subclass of strongly starlike functions Kargar, R. Sokół, J. Mahzoon, H. Complex Variables 30C45, 30C50 Let $\mathcal{S}^*(α_1,α_2)$, where $ α_1, α_2 \in (0,1]$, represent the class of functions $f$ that are analytic in the open unit disk $\mathbb{D}$, normalized by $f(0) = f'(0) - 1=0$, and satisfying the following double-sided inequality: \begin{equation*} -\frac{πα_1}{2}< \arg\left\{\frac{zf'(z)}{f(z)}\right\} <\frac{πα_2}{2}, \quad (z\in\mathbb{D}). \end{equation*} In this manuscript, we estimate the coefficients and logarithmic coefficients associated with functions that belong to the class $\mathcal{S}^*(α_1,α_2)$. As a result, we provide a general bound for the coefficients of a strongly starlike function, which has been an open question until now. Finally, we derive upper and lower bounds for the expression ${\rm Re}\{zf'(z)/f(z)\}$, where $f\in \mathcal{S}^*(α_1,α_2)$. |
| title | On a certain subclass of strongly starlike functions |
| topic | Complex Variables 30C45, 30C50 |
| url | https://arxiv.org/abs/1811.01271 |