On (f, I) - Lacunary statistical convergence of Order α of sequences of sets

Mikail Et,Huseyin Cakalli,Hacer Sengul

doi:10.5269/bspm.v38i7.46259

Mikail Et, Huseyin Cakalli + Show 1 more

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https://doi.org/10.5269/bspm.v38i7.46259

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Abstract

In this paper we introduce the concepts of Wijsman $% \left( f,I\right) -$lacunary statistical{\Large \ }convergence of order $% \alpha $ and Wijsman strongly $\left( f,I\right) -$lacunary statistical% {\Large \ }convergence of order $\alpha ,$ and investigated between their relationship.

Highlights

For any non-empty closed subsets A, Ak ⊂ X, we say that the sequence {Ak} is Wijsman (f, I) −lacunary statistically convergent to A of order α ( or Sθα (f, Iw) −convergent to A ) if for each ε > 0, δ > 0 and x ∈ X, r
For any non-empty closed subsets A, Ak ⊂ X, we say that the sequence {Ak} is said to be Wijsman strongly (f, I) −lacunary statistically convergent to A of order α if for each ε > 0 and x ∈ X, r
1. Let (1) holds, if a sequence is strongly Sθα (f, Iw) −statistically convergent to A

Summary

Introduction

For any non-empty closed subsets A, Ak ⊂ X, we say that the sequence {Ak} is Wijsman (f, I) −lacunary statistically convergent to A of order α ( or Sθα (f, Iw) −convergent to A ) if for each ε > 0, δ > 0 and x ∈ X, r Let f be an unbounded modulus, (X, d) be a metric space, θ be a lacunary sequence, α ∈

Results

Conclusion