Lacunary statistical and lacunary strongly convergence of generalized difference sequences in intuitionistic fuzzy normed linear spaces

Mausumi Sen,Mikail Et

doi:10.5269/bspm.v38i1.34814

Abstract

In this article we introduce the concepts of lacunary statistical convergence and lacunary strongly convergence of generalized difference sequences in intuitionistic fuzzy normed linear spaces and give their characterization. We obtain some inclusion relation relating to these concepts. Further some necessary and sufficient conditions for equality of the sets of statistical convergence and lacunary statistical convergence of generalized difference sequences have been established. The notion of strong Cesaro summability in intuitionistic fuzzy normed linear spaces has been introduced and studied. Also the concept of lacunary generalized difference statistically Cauchy sequence has been introduced and some results are established.

Highlights

Mausumi Sen and Mikail Et abstract: In this article we introduce the concepts of lacunary statistical convergence and lacunary strongly convergence of generalized difference sequences in intuitionistic fuzzy normed linear spaces and give their characterization
Some works in lacunary statistical convergence can be found in ( [2], [15], [16], [18], [26], [27], [29], [33], [36]).The idea of difference sequence was introduced by Kizmaz [21] and later on it was further investigated by different researchers in classical as well as fuzzy sequence spaces ( [3], [4], [6], [9], [10], [11], [35], [37])
The aim of the present paper is to introduce the concepts of lacunary statistical convergence and lacunary strongly convergence of generalized difference sequences in intuitionistic fuzzy normed linear spaces (IFNLS) and obtain some important results on this concept

Summary

Linear Spaces

Mausumi Sen and Mikail Et abstract: In this article we introduce the concepts of lacunary statistical convergence and lacunary strongly convergence of generalized difference sequences in intuitionistic fuzzy normed linear spaces and give their characterization. A sequence x = {xk} in X is said to be lacunary ∆m-statistically convergent to L ∈ X with respect to the intuitionistic fuzzy norm (μ, ν) if, for every ε ∈ (0, 1) and t > 0, δθ({k ∈ N : μ(∆mxk − L, t) ≤ 1 − ε or ν(∆mxk − L, t) ≥ ε}) = 0. In this case we write Sθ(μ,ν) − lim ∆mxk = L. For ε > 0, there exists r0 ∈ N such that

Nr hr

Also the terms

Conclusion