Some New Observations on Wijsman    ℐ   2   -Lacunary Statistical Convergence of Double Set Sequences in Intuitionistic Fuzzy Metric Spaces

Ömer Kişi

doi:10.1155/2021/6897038

Abstract

In this study, we investigate the notions of the Wijsman ℐ 2 -statistical convergence, Wijsman ℐ 2 -lacunary statistical convergence, Wijsman strongly ℐ 2 -lacunary convergence, and Wijsman strongly ℐ 2 -Cesàro convergence of double sequence of sets in the intuitionistic fuzzy metric spaces (briefly, IFMS). Also, we give the notions of Wijsman strongly ℐ 2 ∗ -lacunary convergence, Wijsman strongly ℐ 2 -lacunary Cauchy, and Wijsman strongly ℐ 2 ∗ -lacunary Cauchy set sequence in IFMS and establish noteworthy results.

Highlights

Introduction and BackgroundStatistical convergence was firstly examined by Henry Fast [1]. is notion was redefined for double sequences by Mursaleen and Edely [2]
We investigate the notions of the Wijsman I2-statistical convergence, Wijsman I2-lacunary statistical convergence, Wijsman strongly I2-lacunary convergence, and Wijsman strongly I2-Cesaro convergence of double sequence of sets in the intuitionistic fuzzy Wijsman strongly metric spaces
A sequence 􏽮Fwq􏽯 of nonempty closed subsets of X is known as Wijsman I2-statistical convergent to F or S(I(Wη2,]))-convergent to F with regard to IFM (η, ]), if for every ξ ∈ (0, 1), σ > 0, for each x ∈ X, and for all p > 0

Summary

Introduction and Background

Statistical convergence was firstly examined by Henry Fast [1]. is notion was redefined for double sequences by Mursaleen and Edely [2]. Fridy and Orhan [12] examined the notion of lacunary statistical convergence by using lacunary sequence. Statistical convergence, ideal convergence, and different features of sequences in INFS were examined by several authors [26,27,28,29]. Ulusu and Nuray [31] examined the lacunary statistical convergence of sequence of sets. Convergence for sequences of sets became a notable topic in summability theory after the studies of (see [32,33,34,35,36,37,38]). Lacunary statistical convergence and lacunary strongly convergence for sequence of sets in IFMS were worked by Kisi [39]. Roughout this work, we indicate I2 to be the admissible ideal in N × N, θ2 􏼈(ju, ks)􏼉 to be a double lacunary sequence, (X, η, ], ∗, ◇) to be the IFMS, and F 􏽮Fwq􏽯 to be nonempty closed subsets of X

Main Results

A sequence summable to F

Conclusion