Hemen Dutta

On sequence spaces with elements in a sequence of real linear n-normed spaces

In this work, for an arbitrary sequence space we construct a sequence space with elements in a sequence of real linear n-normed spaces. We investigate the space for Banach space and study some related properties with convergence and completeness.

Strongly (Vλ,A,Δ(vm)n,p)-summable sequence spaces defined by an Orlicz function

Abstract We introduce the strongly ( V λ , A , Δ ( v m ) n , p ) -summable sequences and give the relation between the spaces of strongly ( V λ , A , Δ ( v m ) n , p ) -summable sequences and strongly ( V λ , A , Δ ( v m ) n , p ) -summable sequences with respect to an Orlicz function when A = ( a i k ) is an infinite matrix of complex numbers, Δ ( v m ) n is a generalized difference operator and p = ( p i ) is a sequence of positive real numbers. Also we give natural relationship between strongly ( V λ , A , Δ ( v m ) n , p ) -convergence with respect to an Orlicz function and strongly S λ ( A , Δ ( v m ) n ) -statistical convergence.

On some n-normed linear space valued difference sequences

Abstract The main aim of this article is to extend the notion of strongly Cesaro summable and strongly lacunary summable real sequences to n -normed linear space valued ( n -nls valued) difference sequences. Consequently we introduce the spaces | σ 1 |( X , ∇ ) and N θ ( X , ∇ ), respectively, where X is an n -normed space and ∇ is a difference operator. We investigate these spaces for completeness as well as for the relationship between these spaces.

An Orlicz extension of difference sequences on real linear n-normed spaces

In this paper, we present an extension of some classes of difference sequences by considering them in a base space X, a real linear n-normed space via a sequence of Orlicz functions. We investigate the spaces for linearity, existence of norms and completeness under different conditions. We also show that they are convex spaces and compute their topologically equivalent spaces. Further some results on equivalence of various norms on such extended spaces are presented.MSC:40A05, 46B20, 46B99, 46A19, 46A99.

An Extension of Modular Sequence Spaces

The main aim of this paper is to present an extension of the modular sequence spaces by means of Cesaro mean of order one, to investigate several relevant algebraic and topological properties, and derive some other spaces in the sequel.

Some Orlicz extended ℐ-convergent A-summable classes of sequences of fuzzy numbers

The article introduces some classes of sequences of fuzzy numbers extended by Orlicz functions by using the notions of ℐ-convergence and matrix transformation and investigates the classes for relationship between them as well as establishes some relevant properties. Further, the Hukuhara difference property is employed to derive a new kind of spaces and prove that such spaces can be equipped with a linear topological structure.MSC:40A05, 40D25, 40C05, 46A45.

On Some Sequence Spaces

In this article we introduce some sequence spaces with base space X, a real linear n-normed space. We also use an Orlicz function to construct the spaces. We investigate these spaces for some algebraic and topological structures.

Some classes of Cesàro-type difference sequences over n-normed spaces

In this paper, we introduce some Cesàro-type difference sequences spaces defined over a real linear n-normed space and investigate the spaces for completeness under suitable n-norm in each case. Relevant relations among the classes of sequences are examined. We also introduce the notion of n-BK-spaces and show that the spaces can be made an n-BK-space under certain condition. Further, we compute the Köthe-Toeplitz duals of the spaces, wherever possible within the scope of the research of this article.MSC:40A05, 46A20, 46D05, 46A45, 46E30.

ON SOME N-NORMED SEQUENCE SPACES

In this paper, we introduce the idea of constructing sequence spaces withelements in an n-norm space in comparison with the spacesc0, c, ℓ∞and the Orlicz space ℓMand extend the notion of n-norm to such spaces. Further westate and define some statements about the n-best approximation inn-normed spaces.

Statistical deferred weighted B

The notion of statistical weighted B