Sufficient and necessary conditions for the generalized distribution series to be in subclasses of univalent functions
UDC 517.5 We establish a relationship  between the subclasses of univalent functions and generalized distribution series. The main aim of our  investigation is to obtain  necessary and sufficient conditions for the generalized distribu...
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| Date: | 2023 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2023
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7267 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.5
We establish a relationship  between the subclasses of univalent functions and generalized distribution series. The main aim of our  investigation is to obtain  necessary and sufficient conditions for the generalized distribution series to belong to the classes ${\mathcal{TF}}(\rho,\vartheta),$ $\mathcal{{TH}}(\rho,\vartheta), \,\mathcal{{TJ}}(\rho,\vartheta)$, and $\mathcal{{TX}}(\rho,\vartheta)$. In addition, we obtain some particular cases of our main results. |
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| DOI: | 10.3842/umzh.v75i10.7267 |