Some Euler spaces of difference sequences of order m The present article is partly based on the doctoral thesis of first author

• Published in: Acta mathematica scientia Vol. 27; no. 2; pp. 254 - 266
• Main Authors: Harun, Polat, Feyzi, Başar
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.04.2007
• Subjects: Difference sequence spaces of order m; matrix mappings; Schauder basis; the α-, β-, and γ-duals; matrix mappings; Difference sequence spaces of order m; Schauder basis; the α-, β-, and γ-duals
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(07)60024-1

Kizmaz [13] studied the difference sequence spaces ℓ ∞(Δ), c(Δ), and c0(Δ). Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Altay and Başar [5] and Altay, Başar, and Mursaleen [7] introduced the Euler sequence spaces e r 0, e r c , and e r ∞, respectively. The main purpose of this article is to introduce the spaces e r 0(Δ m ), e r c (Δ m ), and e r ∞(Δ m ) consisting of all sequences whose m th order differences are in the Euler spaces e r 0, e r c , and e r ∞, respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the α-, β-, and γ-duals of the spaces e r 0(Δ m ), e r c (Δ m ), and e r ∞(Δ m ), and the Schauder basis of the spaces e r 0(Δ m ), e r c (Δ m ). The last section of the article is devoted to the characterization of some matrix mappings on the sequence space e r c (Δ m ).