On Rough $\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence for Functions Defined on Amenable Semigroups

Abstract

In this paper, firstly we introduced the concepts of rough $\mathcal{I}$-convergence, rough $\mathcal{I}^*$-convergence, rough $\mathcal{I}$-Cauchy sequence, and rough $\mathcal{I}^*$-Cauchy sequence of a function defined on discrete countable amenable semigroups. Then, we investigated the relations between them.