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| Format: | Preprint |
| Published: |
2018
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| Online Access: | https://arxiv.org/abs/1805.01043 |
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| _version_ | 1866917060059070464 |
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| author | Kargar, Rahim |
| author_facet | Kargar, Rahim |
| contents | We investigate the geometric properties of the Volterra-type integral operator \begin{equation*} T_g[f](z) = \int_{0}^{z} f(s)\, g'(s)\, ds, \quad |z|<1, \end{equation*} acting on various subclasses of analytic functions in the unit disk. Sharp estimates are obtained for the convexity radius of $T_g$, which simultaneously determine its univalence radius, across several classical function families. In addition, we introduce and study higher-order Volterra-type operators, establish their normalized forms, and propose an open question on the scaling behavior of their convexity radii. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1805_01043 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Volterra type integral operator and analytic function spaces Kargar, Rahim Complex Variables 47B38, 30C45 We investigate the geometric properties of the Volterra-type integral operator \begin{equation*} T_g[f](z) = \int_{0}^{z} f(s)\, g'(s)\, ds, \quad |z|<1, \end{equation*} acting on various subclasses of analytic functions in the unit disk. Sharp estimates are obtained for the convexity radius of $T_g$, which simultaneously determine its univalence radius, across several classical function families. In addition, we introduce and study higher-order Volterra-type operators, establish their normalized forms, and propose an open question on the scaling behavior of their convexity radii. |
| title | Volterra type integral operator and analytic function spaces |
| topic | Complex Variables 47B38, 30C45 |
| url | https://arxiv.org/abs/1805.01043 |