On $\Cal{I}$ and $\Cal{I}^*$-equal convergence and an Egoroff-type theorem

Pratulananda Das, Sudipta Dutta, Sudip Kumar Pal

In this paper we extend the notion of equal convergence of Császár and Laczkovich with the help of ideals of the set of positive integers and introduce the ideas of $\Cal{I}$ and $\Cal{I}^*$-equal convergence and prove certain properties. Throughout the investigation two classes of ideals, one satisfying ``Chain Condition'' and another called $P$-ideals play a very important role. We also introduce certain related notions of convergence and prove an Egoroff-type theorem for $\Cal{I}^*$-equal convergence.