I-convergence of sequences in metric-like spaces

TL;DR

This paper introduces and explores the concepts of I-convergence and I*-convergence of sequences within metric-like spaces, analyzing their properties and relationships.

Contribution

It presents new definitions of I-convergence and I*-convergence in metric-like spaces and investigates their interconnections.

Findings

I-convergence and I*-convergence are related in metric-like spaces

New properties of I-convergence are established

The relationship between I-convergence and I*-convergence is characterized

Abstract

In this paper we introduce and study the notion of I-convergence of sequences in a metric-like space, where I is an ideal of subsets of the set N of all natural numbers. Further introducing the notion of I*-convergence of sequences in a metric-like space we study its relationship with I-convergence.