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

Abstract

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