In this article, using generalized weighted mean and difference matrix of order m, we introduce the paranormed sequence space l(u, v, p; △(m)), which consist of the sequences whose generalized weighted △(m)-di...In this article, using generalized weighted mean and difference matrix of order m, we introduce the paranormed sequence space l(u, v, p; △(m)), which consist of the sequences whose generalized weighted △(m)-difference means are in the linear space l(p) defined by I.J.Maddox. Also, we determine the basis of this space and compute its α-, β- and γ-duals. Further, we give the characterization of the classes of matrix mappings from l(u, v, p, △(m)) to l∞, c, and co. Finally, we apply the Hausdorff measure of noncompacness to characterize some classes of compact operators given by matrices on the space lp(U, v, △(m)) (1 ≤ p 〈 ∞).展开更多
Kizmaz [13] studied the difference sequence spaces ∞(A), c(A), and co(A). Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Alta...Kizmaz [13] studied the difference sequence spaces ∞(A), c(A), and co(A). 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 e0^r, ec^r, and e∞^r, respectively. The main purpose of this article is to introduce the spaces e0^r△^(m)), ec^r△^(m)), and e∞^r△^(m))consisting of all sequences whose mth order differences are in the Euler spaces e0^r, ec^r, 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 e0^r△^(m)), ec^r△^(m)), and e∞^r△^(m)), and the Schauder basis of the spaces e0^r△^(m)), ec^r△^(m)). The last section of the article is devoted to the characterization of some matrix mappings on the sequence space ec^r△^(m)).展开更多
文摘In this article, using generalized weighted mean and difference matrix of order m, we introduce the paranormed sequence space l(u, v, p; △(m)), which consist of the sequences whose generalized weighted △(m)-difference means are in the linear space l(p) defined by I.J.Maddox. Also, we determine the basis of this space and compute its α-, β- and γ-duals. Further, we give the characterization of the classes of matrix mappings from l(u, v, p, △(m)) to l∞, c, and co. Finally, we apply the Hausdorff measure of noncompacness to characterize some classes of compact operators given by matrices on the space lp(U, v, △(m)) (1 ≤ p 〈 ∞).
文摘Kizmaz [13] studied the difference sequence spaces ∞(A), c(A), and co(A). 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 e0^r, ec^r, and e∞^r, respectively. The main purpose of this article is to introduce the spaces e0^r△^(m)), ec^r△^(m)), and e∞^r△^(m))consisting of all sequences whose mth order differences are in the Euler spaces e0^r, ec^r, 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 e0^r△^(m)), ec^r△^(m)), and e∞^r△^(m)), and the Schauder basis of the spaces e0^r△^(m)), ec^r△^(m)). The last section of the article is devoted to the characterization of some matrix mappings on the sequence space ec^r△^(m)).