On $\mathcal{I}$-convergence of sequences of functions and uniform conjugacy

TL;DR

This paper introduces new types of convergence for sequences of functions based on ideals and investigates their properties and preservation under uniform conjugacy.

Contribution

It defines $ ext{I}^*$-$ ext{alpha}$-uniform equal convergence and explores their lattice properties and invariance under uniform conjugacy.

Findings

Defined $ ext{I}^*$-$ ext{alpha}$-uniform equal convergence.

Established lattice properties of the convergence classes.

Proved invariance of convergence notions under uniform conjugacy.

Abstract

In this paper we introduce the notion of $\mathcal{I^*}\text{-}\alpha$-uniform equal convergence and $\mathcal{I^*}\text{-}\alpha$-strong uniform equal convergence of sequences of functions and then investigate some lattice properties of $\Phi ^{\mathcal{I^*}\text{-}\alpha\text{-}u.e.}$ and $\Phi ^{\mathcal{I^*}\text{-}\alpha \text{-}s.u.e.}$, the classes of all functions which are $\mathcal{I^*}\text{-}\alpha$-uniform equal limits and $\mathcal{I^*}\text{-}\alpha$-strong uniform equal limits of sequences of functions respectively obtained from a class of functions $\Phi$. We have also shown that $\mathcal{I}$-exhaustiveness, $\mathcal{I}$-uniform and $\mathcal{I}\text{-}\alpha$- convergence of sequences of functions are preserved under uniform conjugacy