Euler-Ces`aro difference spaces of bounded, convergent and null sequences

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Published: Dec 30, 2016
DOI: https://doi.org/10.5556/j.tkjm.47.2016.2065
Keywords:
Composition of summability methods Ces\`{a}ro mean of order one Euler mean of order one backward difference operator sequence space BK space Schauder basis Köthe-Toeplitz duals matrix transformations

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Feyzi Basar
Naim L. Braha

Abstract

In this paper, we introduce the spaces $\breve{\ell}_{\infty}$, $\breve{c}$ and $\breve{c}_{0}$ of Euler-Ces`aro bounded, convergent and null difference sequences and prove that the inclusions $\ell_{\infty}\subset\breve{\ell}_{\infty}$, $c\subset\breve{c}$ and $c_{0}\subset\breve{c}_{0}$ strictly hold. We show that the spaces $\breve{c}_{0}$ and $\breve{c}$ turn out to be the separable BK spaces such that $\breve{c}$ does not possess any of the following: AK property and monotonicity. We determine the alpha-, beta- and gamma-duals of the new spaces and characterize the matrix classes $(\breve{c}:\ell_{\infty})$, $(\breve{c}:c)$ and $(\breve{c}:c_0)$.

 

 

Article Details

How to Cite
Basar, F., & Braha, N. L. (2016). Euler-Ces`aro difference spaces of bounded, convergent and null sequences. Tamkang Journal of Mathematics, 47(4), 405–420. https://doi.org/10.5556/j.tkjm.47.2016.2065
Issue
Vol. 47 No. 4 (2016)
Section
Papers
Author Biographies

Feyzi Basar

KısıklıMah. Alim Sok. Alim Apt. No: 7/6, 34692 - Üsküdar/˙Istanbul, Turkey.

Naim L. Braha

Department ofMathematics and Computer Sciences, University of Prishtina, Avenue “Mother Teresa", No=5, Prishtine, 10000, Kosova.

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