Density by moduli and Wijsman statistical convergence

TL;DR

This paper extends Wijsman statistical convergence for closed sets in metric spaces by introducing $f$-Wijsman convergence with unbounded moduli, and explores its relation to Wijsman strong Cesàro summability.

Contribution

It introduces the concept of $f$-Wijsman statistical convergence and investigates its properties and relationship with Wijsman strong Cesàro summability.

Findings

Wijsman convergent sequences are exactly those $f$-Wijsman statistically convergent for all unbounded moduli.

Established the relationship between $f$-Wijsman statistical convergence and Wijsman strong Cesàro summability.

Generalized the notion of statistical convergence using unbounded moduli in the context of Wijsman convergence.

Abstract

In this paper, we generalized the Wijsman statistical convergence of closed sets in metric space by introducing the $f$-Wijsman statistical convergence these of sets, where $f$ is an unbounded modulus. It is shown that the Wijsman convergent sequences are precisely those sequences which are $f$-Wijsman statistically convergent for every unbounded modulus $f$. We also introduced a new concept of Wijsman strong Ces\`{a}ro summability with respect to a modulus, and investigate the relationships between the $f$-Wijsman statistically convergent sequences and the Wijsman strongly Ces\`{a}ro summable sequences with respect to $f$.