On the Gelfond – Leont’ev – Sǎlǎgean and Gelfond – Leont’ev – Ruscheweyh operators and analytic continuation of functions
UDC 517.537 Let $A_{\lambda} (0)$ denote the class of power series $g(z) = \sum^{\infty}_{k=0} g^k z_k$ such that $|g_k| \leq \lambda_k| g_1|$ for all $k \geq 1$, where $\lambda = (\lambda_k)$ is a sequence of positive numbers. We obtain necessary and sufficient conditions imposed on a function $l$...
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| Дата: | 2022 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Українська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2022
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/7058 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Резюме: | UDC 517.537
Let $A_{\lambda} (0)$ denote the class of power series $g(z) = \sum^{\infty}_{k=0} g^k z_k$ such that $|g_k| \leq \lambda_k| g_1|$ for all $k \geq 1$, where $\lambda = (\lambda_k)$ is a sequence of positive numbers. We obtain necessary and sufficient conditions imposed on a function $l$ and an increasingsequence $(n_p)$ of non-negative integers ensuring that the assumption that the Gelfond – Leont’ev – Sălăgean derivative $D^{n_p}_{l,[S]}f $ and the Gelfond – Leont’ev – Ruscheweyh derivative $D^{n_p}_{l,[R]}f $ belong to the class $A_{\lambda} (0)$ for all $p \in {\Bbb Z}_+$ implies that f is an entire function. |
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| DOI: | 10.37863/umzh.v74i5.7058 |