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 - <p style="text-align: justify;">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 $0&lt;p&lt;1$, 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 $(\varepsilon^{r,s}_p:\mathcal{M}_u)$,&nbsp;$(\varepsilon^{r,s}_p:\mathcal{C}_{bp})$&nbsp;and $(\varepsilon^{r,s}_p:\mathcal{L}_q)$ of four
dimensional matrix transformations, where $1≤q&lt;∞$. Finally, we shortly emphasize on
the Euler spaces of single and double sequences, and note some further suggestions.</p>