Necessary and sufficient Tauberian conditions under which convergence follows from $A^{r,\delta}$ summability
Let $x=(x_{mn})$ be a double sequence of real or complex numbers. The $A^{r,\delta}$-transform of a sequence $(x_{mn})$ is defined by $$ (A^{r,\delta}x)_{mn}={\sigma^{r,\delta}_{mn}(x)}=\frac{1}{(m+1)(n+1)}\sum_{j=0}^{m}\sum_{k=0}^{n}(1+r^j)(1+\delta^k)x_{jk}, \ \ \ \ \ 0<r, \delta<1 $$ The $...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Sociedade Brasileira de Matemática
2022-12-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Online Access: | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/50823 |