Year: 2018
Analysis in Theory and Applications, Vol. 34 (2018), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-2017-0056
Analysis in Theory and Applications, Vol. 34 (2018), Iss. 3 : pp. 241–252
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Summability theory double sequences double series alpha- beta- and gamma-duals matrix domain of 4-dimensional matrices matrix transformations.