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Volume 34, Issue 3
Domain of Euler Mean in the Space of Absolutely $p$-Summable Double Sequences with $0< p<1$

Medine Yeşilkayagil & Feyzi Başar

Anal. Theory Appl., 34 (2018), pp. 241-252.

Published online: 2018-11

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  • Abstract

In this study, as the domain of four dimensional Euler mean $E(r,s)$ of orders $r$, $s$ in the space $\mathcal{L}_p$ for $0<p<1$, we examine the double sequence space $\varepsilon^{r,s}_p$ and some properties of four dimensional Euler mean. We determine the $α$- and $β(bp)$-duals of the space $\varepsilon^{r,s}_p$, and characterize the classes $(\varepsilon^{r,s}_p:\mathcal{M}_u)$, $(\varepsilon^{r,s}_p:\mathcal{C}_{bp})$ and $(\varepsilon^{r,s}_p:\mathcal{L}_q)$ of four dimensional matrix transformations, where $1≤q<∞$. Finally, we shortly emphasize on the Euler spaces of single and double sequences, and note some further suggestions.

  • AMS Subject Headings

46A45, 40C05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-34-241, author = {Medine Yeşilkayagil and Feyzi Başar}, title = {Domain of Euler Mean in the Space of Absolutely $p$-Summable Double Sequences with $0< p<1$}, journal = {Analysis in Theory and Applications}, year = {2018}, volume = {34}, number = {3}, pages = {241--252}, abstract = {

In this study, as the domain of four dimensional Euler mean $E(r,s)$ of orders $r$, $s$ in the space $\mathcal{L}_p$ for $0<p<1$, we examine the double sequence space $\varepsilon^{r,s}_p$ and some properties of four dimensional Euler mean. We determine the $α$- and $β(bp)$-duals of the space $\varepsilon^{r,s}_p$, and characterize the classes $(\varepsilon^{r,s}_p:\mathcal{M}_u)$, $(\varepsilon^{r,s}_p:\mathcal{C}_{bp})$ and $(\varepsilon^{r,s}_p:\mathcal{L}_q)$ of four dimensional matrix transformations, where $1≤q<∞$. Finally, we shortly emphasize on the Euler spaces of single and double sequences, and note some further suggestions.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2017-0056}, url = {http://global-sci.org/intro/article_detail/ata/12839.html} }
TY - JOUR T1 - Domain of Euler Mean in the Space of Absolutely $p$-Summable Double Sequences with $0< p<1$ AU - Medine Yeşilkayagil & Feyzi Başar JO - Analysis in Theory and Applications VL - 3 SP - 241 EP - 252 PY - 2018 DA - 2018/11 SN - 34 DO - http://doi.org/10.4208/ata.OA-2017-0056 UR - https://global-sci.org/intro/article_detail/ata/12839.html KW - Summability theory, double sequences, double series, alpha-, beta- and gamma-duals, matrix domain of 4-dimensional matrices, matrix transformations. AB -

In this study, as the domain of four dimensional Euler mean $E(r,s)$ of orders $r$, $s$ in the space $\mathcal{L}_p$ for $0<p<1$, we examine the double sequence space $\varepsilon^{r,s}_p$ and some properties of four dimensional Euler mean. We determine the $α$- and $β(bp)$-duals of the space $\varepsilon^{r,s}_p$, and characterize the classes $(\varepsilon^{r,s}_p:\mathcal{M}_u)$, $(\varepsilon^{r,s}_p:\mathcal{C}_{bp})$ and $(\varepsilon^{r,s}_p:\mathcal{L}_q)$ of four dimensional matrix transformations, where $1≤q<∞$. Finally, we shortly emphasize on the Euler spaces of single and double sequences, and note some further suggestions.

Medine Yeşilkayagil and Feyzi Başar. (2018). Domain of Euler Mean in the Space of Absolutely $p$-Summable Double Sequences with $0< p<1$. Analysis in Theory and Applications. 34 (3). 241-252. doi:10.4208/ata.OA-2017-0056
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