Abstract
In this article, we shall introduce a new class of ideal convergent (briefly I-convergent) sequence spaces using, infinite matrix, an Orlicz function and difference operator defined on n-normed spaces. We study these spaces for some linear topological structures and algebraic properties. We also give some relations related to these sequence spaces.Mathematics Subject Classification 2010: 40A05; 40B50; 46A19; 46A45.
Highlights
1 Introduction The idea of statistical convergence was given by Zygmund [1] in the first edition of his monograph published in Warsaw in 1935
The idea is based on the notion of natural density of subsets of N, the set of positive integers, which is defined as follows: The natural density of a subset E of natural numbers is denoted by δ(E) and is defined by δ(E) = lim 1 |{k ∈ E : k ≤ n}|, n→∞ n where the vertical bar denotes the cardinality of the enclosed set
Note that I-convergence is an interesting generalization of statistical convergence
Summary
The idea of statistical convergence was given by Zygmund [1] in the first edition of his monograph published in Warsaw in 1935. The notion of difference sequence space was introduced by Kizmaz [10]. For a non negative integer s, the generalized difference sequence spaces are defined as follows: For a given sequence space X we have
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