TY - JOUR T1 - Domain of Euler Mean in the Space of Absolutely $p$-Summable Double Sequences with $0< p<1$ 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.