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

Harun P.Feyzi B.2024-08-042024-08-0420070252-9602https://doi.org/10.1016/S0252-9602(07)60024-1https://hdl.handle.net/11616/90545Kizmaz [13] studied the difference sequence spaces ??(?), c(?), and c0(?). 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 er0, erc, and er?, respectively. The main purpose of this article is to introduce the spaces er0(?m), erc(?m), and er?(?m) consisting of all sequences whose mth order differences are in the Euler spaces er0, erc, and er?, respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the ?-, ?-, and ?-duals of the spaces er0(?m), erc(?m), and er?(?m), and the Schauder basis of the spaces er0(?m), erc(?m). The last section of the article is devoted to the characterization of some matrix mappings on the sequence space erc(?m). © 2007 Wuhan Institute of Physics and Mathematics.eninfo:eu-repo/semantics/closedAccessDifference sequence spaces of order mmatrix mappingsSchauder basisthe ?-, ?-, and ?-dualsSome Euler spaces of difference sequences of order m* * The present article is partly based on the doctoral thesis of first authorArticle27225426610.1016/S0252-9602(07)60024-12-s2.0-34248231796Q2