On I and I∗-equal convergence and an Egoroff-type theorem

Abstract

In this paper we extend the notion of equal convergence ofCsászár and Laczkovich with the help of ideals of the set ofpositive integers and introduce the ideas of $\mathcal{I}$ and${\mathcal{I}}^{\mathcal{\ast }}$-equal convergence and prove certain properties.Throughout the investigation two classes of ideals, onesatisfying "Chain Condition'' and another called $P$-ideals playa very important role. We also introduce certain related notionsof convergence and prove an Egoroff-type theorem for${\mathcal{I}}^{\mathcal{\ast }}$-equal convergence.