[ℓp]e.r Euler-Riesz Difference Sequence Spaces
![${[\ell_p]}_{e.r}$ 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 ˘ℓ∞, ˘c and ˘c0 of Euler-Cesáro bounded, convergent and null difference sequences and studied their some properties. Then, in [2], we introduced the sequence spaces [ℓ∞]e.r,[c]e.r and [c0]e.r of Euler-Riesz bounded, convergent and null difference sequences by using the composition of the Euler mean E1 and Riesz mean Rq with backward difference operator Δ. The main purpose of this study is to introduce the sequence space [ℓp]e.r of Euler-Riesz p−absolutely convergent series, where 1≤p<∞, difference sequences by using the composition of the Euler mean E1 and Riesz mean Rq with backward difference operator Δ. Furthermore, the inclusion ℓp⊂[ℓp]e.r hold, the basis of the sequence space [ℓp]e.r is constructed and α−, β− and γ−duals of the space are determined. Finally, the classes of matrix transformations from the [ℓp]e.r Euler-Riesz difference sequence space to the spaces ℓ∞,c and c0 are characterized. We devote the final section of the paper to examine some geometric properties of the space [ℓp]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 β−duals matrix transformations.
Author Details
Hacer Bilgin Ellidokuzoğlu Email
Serkan Demiriz Email
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