![${[\ell_p]}_{e.r}$ Euler-Riesz Difference Sequence Spaces](https://global-sci.com/images/articles/73792.png?w=900&h=&fit=&c=2&assets_cache=20241112042820&bg=white)
Year: 2021
Author: Hacer Bilgin Ellidokuzoğlu, Serkan Demiriz
Analysis in Theory and Applications, Vol. 37 (2021), Iss. 4 : pp. 557–571
Abstract
Başar and Braha [1], introduced the sequence spaces $\breve{\ell}_\infty$, $\breve{c}$ and $\breve{c}_0$ of Euler-Cesáro bounded, convergent and null difference sequences and studied their some properties. Then, in [2], we introduced the sequence spaces ${[\ell_\infty]}_{e.r}, {[c]}_{e.r}$ and ${[c_0]}_{e.r}$ of Euler-Riesz bounded, convergent and null difference sequences by using the composition of the Euler mean $E_1$ and Riesz mean $R_q$ with backward difference operator $\Delta$. The main purpose of this study is to introduce the sequence space ${[\ell_p]}_{e.r}$ of Euler-Riesz $p-$absolutely convergent series, where $1 \leq p <\infty$, difference sequences by using the composition of the Euler mean $E_1$ and Riesz mean $R_q$ with backward difference operator $\Delta$. Furthermore, the inclusion $\ell_p\subset{[\ell_p]}_{e.r}$ hold, the basis of the sequence space ${[\ell_p]}_{e.r}$ is constructed and $\alpha-$, $\beta-$ and $\gamma-$duals of the space are determined. Finally, the classes of matrix transformations from the ${[\ell_p]}_{e.r}$ Euler-Riesz difference sequence space to the spaces $\ell_\infty, c$ and $c_0$ are characterized. We devote the final section of the paper to examine some geometric properties of the space ${[\ell_p]}_{e.r}$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-2017-0068
Analysis in Theory and Applications, Vol. 37 (2021), Iss. 4 : pp. 557–571
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Composition of summability methods Riesz mean of order one Euler mean of order one backward difference operator sequence space BK space Schauder basis $\beta-$duals matrix transformations.
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