Lacunary Statistical Convergence in Fuzzy Normed Linear Spaces

Muhammed Recai Turkmen

doi:10.11648/j.acm.20170605.13

Abstract

In this paper, it is introduced the concept of lacunary statistical convergence with respect to a fuzzy norm by using lacunary statistical convergence of a sequence and statistical convergent of a sequence with respect to fuzzy norm. It also has studied the relation between these concepts.

Highlights

The concept of statistical convergence of real number sequences was introduced Fast [7] and Steinhaus [18] and later reintroduced by Schoenberg [15] independently
The purpose of this paper is to introduce and study a concept of lacunary convergence sequence with respect to fuzzy norm
We introduced the concept of lacunary statistical convergence with respect to a fuzzy norm

Summary

Introduction

The concept of statistical convergence of real number sequences was introduced Fast [7] and Steinhaus [18] and later reintroduced by Schoenberg [15] independently. A sequence ( xk ) in X is statistically convergent to L ∈ X with respect to the fuzzy norm on X provided that for each ε > 0 , we have ({ }) ( ) δ k ∈ N : D xk − L ,0ɶ ≥ ε = 0 (3). Some arithmetic operations for α − level sets are defined as follows: u, v ∈ L(R) and [u]α = uα− , uα+ and [v]α = vα− , vα+ , α ∈ Sençimen [17] was defined convergence in fuzzy normed spaces by taking advantage of Kaleva [11, 8], as follows;. The purpose of this paper is to introduce and study a concept of lacunary convergence sequence with respect to fuzzy norm

Definition

Theorem

Conclusion