Some Tauberian theorems for the weighted mean method of summability of double sequence
UDC 517.5 Let $p=(p_j)$ and $q=(q_k)$ be real sequences of nonnegative numbers with the property that $P_m=\sum _{j=0}^{m} p_j \neq 0$ and $Q_n=\sum _{k=0}^{n} q_k \neq 0$ for all $m$ and $n.$ Let $(P_m)$ and $(Q_n)$ be regulary varying positive indices. Assume that $(u_{mn})$ is a doub...
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| Дата: | 2023 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2023
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/509 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | UDC 517.5
Let $p=(p_j)$ and $q=(q_k)$ be real sequences of nonnegative numbers with the property that $P_m=\sum _{j=0}^{m} p_j \neq 0$ and $Q_n=\sum _{k=0}^{n} q_k \neq 0$ for all $m$ and $n.$ Let $(P_m)$ and $(Q_n)$ be regulary varying positive indices. Assume that $(u_{mn})$ is a double sequence of complex (real) numbers, which is $(\overline{N},p,q; \alpha,\beta)$ summable with a finite limit, where $(\alpha,\beta)=(1,1)$, $(1,0)$, or $(0,1)$.  We present some conditions imposed on the weights under which  $(u_{mn})$ converges in Pringsheim's sense.  These results generalize and extend the results obtained by authors in [Comput. Math. Appl., 62, No. 6, 2609–2615 (2011)]. |
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| DOI: | 10.3842/umzh.v75i9.509 |