Generalized difference sequence spaces associated with a multiplier sequence on a real n-normed space

The purpose of this paper is to introduce new sequence spaces associated with a multiplier sequence by using an infinite matrix, an Orlicz function and a generalized B-difference operator on a real n-normed space. Some topological properties of these spaces are examined. We also define a new concept, which will be called (B-Lambda(mu))(n)-statistical A-convergence, and establish some inclusion connections between the sequence space W(A, B-Lambda(mu), p, parallel to., ... , .parallel to) and the set of all (B-Lambda(mu))(n)-statistically A-convergent sequences

Inclusion theorems of double Deferred Cesàro means II

In 1932 R. P. Agnew present a definition for Deferred Ces`aro mean. Using this definition R. P. Agnew present inclusion theorems for the deferred and none Deferred Ces`aro means. This paper is part 2 of a series of papers that present extensions to the notion of double Deferred Ces`aro means. Similar to part 1 this paper uses this definition and the notion of regularity for four dimensional matrices, to present extensions and variations of the inclusion theorems presented by R. P. Agnew in [2]

On Some Generalized -Difference Riesz Sequence Spaces and Uniform Opial Property

We define the new generalized difference Riesz sequence spaces r(infinity)(q)(p, B-m), r(c)(q)(p, B-m), and r(0)(q)(p, B-m) which consist of all the sequences whose B-m-transforms are in the Riesz sequence spaces r(infinity)(q)(p), r(c)(q)(p), and r(0)(q)(p), respectively, introduced by Altay and Basar (2006). We examine some topological properties and compute the alpha-, beta-, and gamma-duals of the spaces r(infinity)(q)(p, B-m), r(c)(q)(p, B-m), and r(0)(q)(p, B-m). Finally, we determine the necessary and sufficient conditions on the matrix transformation from the spaces r(infinity)(q)(p, B-m), r(c)(q)(p, B-m), and r(0)(q)(p, B-m) to the spaces l(infinity) and c and prove that sequence spaces r(0)(q)(p, B-m) and r(c)(q)(p, B-m) have the uniform Opial property for p(k) <= 1 for all k is an element of N.https://doi.org/10.1155/2011/48573

ON SOME DIFFERENCE SEQUENCE SPACES OF WEIGHTED MEANS AND COMPACT OPERATORS

In the peresent paper, by using generalized weighted mean and difference matrix of order m, we introduce the sequence spaces X(u, v, Delta((m))), where X is one of the spaces l(infinity), c or c(0). Also, we determine the alpha-, beta- and gamma-duals of those spaces and construct their Schauder bases for X is an element of {c, c(0)}. Morever, we give the characterization of the matrix mappings on the spaces X(u, v, Delta(m)) for X is an element of {l(infinity), c, c(0)}. Finally, we characterize some classes of compact operators on the spaces l(1) (u, v, Delta(m)) and c(0)(u, v, Delta(m)) by using the Hausdorff measure of noncompactness

Weighted Lacunary Statistical Convergence in Locally Solid Riesz Spaces

In this paper we introduce the concepts of weighted lacunary statistical tau-convergence, weighted lacunary statistical tau-bounded by combining both of the definitions of lacunary sequence and Norlund-type mean, using a new lacunary sequence which has been defined by Basarir and Konca [3]. We also prove some topological results related to these concepts in the framework of locally solid Riesz spaces.https://doi.org/10.2298/FIL1410059

ON THE GENERALIZED RIESZ B-DIFFERENCE SEQUENCE SPACES

In this paper, we define the new generalized Riesz B-difference sequence spaces r(infinity)(q) (p, B), r(c)(q) (p, B), r(0)(q) (p, B) and r(q) (p,B) which consist of the sequences whose R(q)B-transforms are in the linear spaces l(infinity) (p), c (p), c(0) (p) and l (p), respectively, introduced by I.J.Maddox [8], [9]. We give some topological properties and compute the alpha-, beta- and gamma-duals of these spaces. Also we determine the neccesary and sufficient conditions on the matrix transformations from these spaces into l(infinity) and c

On some new sequence spaces of fuzzy numbers

In this paper, we introduce and study some new sequence spaces of fuzzy numbers generated by non-negative regular matrix A = (a(nk)) (n, k = 1, 2)