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

Abstract

In this paper we introduce the notion of ${\mathcal{I}}^{\ast }\text{-}\alpha$-uniform equal convergence and ${\mathcal{I}}^{\ast }\text{-}\alpha$-strong uniform equal convergence of sequences of functions and then investigate some lattice properties of ${\Phi }^{{\mathcal{I}}^{\ast }\text{-}\alpha \text{-}u.e.}$ and ${\Phi }^{{\mathcal{I}}^{\ast }\text{-}\alpha \text{-}s.u.e.}$, the classes of all functions which are ${\mathcal{I}}^{\ast }\text{-}\alpha$-uniform equal limits and ${\mathcal{I}}^{\ast }\text{-}\alpha$-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

11 pages