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

doi:10.4208/ata.OA-2017-0056

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

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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

Pages: 12

Keywords: Summability theory double sequences double series alpha- beta- and gamma-duals matrix domain of 4-dimensional matrices matrix transformations.

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