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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} }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.