Density by moduli and Wijsman statistical convergence

Abstract

In this paper, we have generalized the Wijsman statistical convergence of closed sets in metric space by introducing the $f$-Wijsman statistical convergence of these 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 have also introduced a new concept of Wijsman strong Cesàro summability with respect to a modulus $f$, and investigate the relationship between the $f$-Wijsman statistically convergent sequences and the Wijsman strongly Cesàro summable sequences with respect to $f$.