数学物理学报(英文版)

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SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m

Harun Polat; Feyzi Basar   

  1. Inonu Universitesi Adiyaman Fen-Edebiyat Fakultesi, 02040-Adiyaman, Turkey
  • 收稿日期:2003-12-24 修回日期:1900-01-01 出版日期:2007-04-20 发布日期:2007-04-20
  • 通讯作者: Harun Polat

SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m

Harun Polat; Feyzi Basar   

  1. Inonu Universitesi Adiyaman Fen-Edebiyat Fakultesi, 02040-Adiyaman, Turkey
  • Received:2003-12-24 Revised:1900-01-01 Online:2007-04-20 Published:2007-04-20
  • Contact: Harun Polat

摘要:

Kizmaz [13] studied the difference sequence spaces $\ell_\infty(\Delta),~c(\Delta)$, and $c_0(\Delta)$. Several article dealt with the sets of sequences of $m$-th order difference of which are bounded, convergent, or convergent to zero. Altay and Ba\c sar [5] and Altay, Ba\c sar, and Mursaleen [7] introduced the Euler sequence spaces $e_0^r$, $e_c^r$, and $e_\infty^r$, respectively. The main purpose of this article is to introduce the spaces $e_0^r(\Delta^{(m)})$, $e_c^r(\Delta^{(m)})$, and $e_\infty^r(\Delta^{(m)})$ consisting of all sequences whose $m^{th}$ order differences are in the Euler spaces $e_0^r$, $e_c^r$, and $e_\infty^r$, respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the $\alpha$-, $\beta$-, and $\gamma$-duals of the spaces $e_0^r(\Delta^{(m)})$, $e_c^r(\Delta^{(m)})$, and $e_\infty^r(\Delta^{(m)})$, and the Schauder basis of the spaces $e_0^r(\Delta^{(m)})$, $e_c^r(\Delta^{(m)})$. The last section of the article is devoted to the characterization of some matrix mappings on the sequence space $e_c^r(\Delta^{(m)})$.

关键词: Difference sequence spaces of order m, Schauder basis, the α-, β-, and γ-duals, matrix mappings

Abstract:

Kizmaz [13] studied the difference sequence spaces $\ell_\infty(\Delta),~c(\Delta)$, and $c_0(\Delta)$. Several article dealt with the sets of sequences of $m$-th order difference of which are bounded, convergent, or convergent to zero. Altay and Ba\c sar [5] and Altay, Ba\c sar, and Mursaleen [7] introduced the Euler sequence spaces $e_0^r$, $e_c^r$, and $e_\infty^r$, respectively. The main purpose of this article is to introduce the spaces $e_0^r(\Delta^{(m)})$, $e_c^r(\Delta^{(m)})$, and $e_\infty^r(\Delta^{(m)})$ consisting of all sequences whose $m^{th}$ order differences are in the Euler spaces $e_0^r$, $e_c^r$, and $e_\infty^r$, respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the $\alpha$-, $\beta$-, and $\gamma$-duals of the spaces $e_0^r(\Delta^{(m)})$, $e_c^r(\Delta^{(m)})$, and $e_\infty^r(\Delta^{(m)})$, and the Schauder basis of the spaces $e_0^r(\Delta^{(m)})$, $e_c^r(\Delta^{(m)})$. The last section of the article is devoted to the characterization of some matrix mappings on the sequence space $e_c^r(\Delta^{(m)})$.

Key words: Difference sequence spaces of order m, Schauder basis, the α-, β-, and γ-duals, matrix mappings

中图分类号: 

  • 46A45