I^K-convergence

TL;DR

This paper introduces I^K-convergence, a generalized concept encompassing sequences, double sequences, and nets, and demonstrates that many existing results for these special cases also hold for I^K-convergence.

Contribution

The paper presents a new generalized convergence concept, I^K-convergence, unifying various types of convergence and extending previous results to this broader framework.

Findings

Many results for sequences, double sequences, and nets are valid for I^K-convergence.

I^K-convergence generalizes existing convergence notions.

The paper establishes foundational properties of I^K-convergence.

Abstract

In this paper we introduce I^K-convergence which is a common generalization of the I^K-convergence of sequences, double sequences and nets. We show that many results that were shown before for these special cases are true for the I^K-convergence, too