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Some Euler spaces of difference sequences of order m
(Springer, 2007) Polat, Harun; Basar, Feyzi
Kizmaz [13] studied the difference sequence spaces l(infinity)(Delta), c(Delta), and c(o)(Delta). Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Altay and Basar [5] and Altay, Basar, and Mursaleen [7] introduced the Euler sequence spaces e(o)(r), e(c)(r), and e(infinity)(r), respectively. The main purpose of this article is to introduce the spaces e(o)(r)(Delta((m))), e(c)(r)(Delta((m))), and e(infinity)(r)(Delta((m))) consisting of all sequences whose m(th) order differences are in the Euler spaces e(o)(r), e(c)(r), and e(infinity)(r), respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the alpha-, beta-, and gamma-duals of the spaces e(o)(r)(Delta((m))), e(c)(r)(Delta((m))), and e(infinity)(r)(Delta((m))), and the Schauder basis of the spaces e(o)(r)(Delta((m))), e(c)(r)(Delta((m))). The last section of the article is devoted to the characterization of some matrix mappings on the sequence space e(c)(r)(Delta((m))).