On set-convergence statistically modulated

TL;DR

This paper investigates convergence concepts for sets using modern summability techniques, focusing on the relationship between Wijsman $f$-statistical and $f$-strong Cesàro convergence when a density-inducing modulus function is involved.

Contribution

It establishes connections between different set-convergence notions derived from summability methods using modulus functions that induce density.

Findings

Wijsman $f$-statistical convergence and $f$-strong Cesàro convergence are related under certain conditions.

The study clarifies how summability methods influence set-convergence notions.

The results extend the understanding of convergence in the context of modern summability and set theory.

Abstract

We explore some convergence notions for set-convergence coming from modern summability methods. Specifically we will see the connections between Wijsman $f$-statistical convergence and Wijsman $f$-strong Ces\`aro convergence, when $f$ is a modulus function that induces a density in $\mathbb{N}$.