Abstract
In this paper we firstly introduce and study the concepts of
\linebreak $\mathcal{I}$-convergence,
$\mathcal{I}^*$-convergence,
$\mathcal{I}$-Cauchy sequence and
$\mathcal{I}^*$-Cauchy sequence of functions
defined on discrete countable amenable groups, where
$\mathcal{I}$ is an ideal of subsets of the amenable
semigroup $G$. Secondly, we introduce and examine
$\mathcal{I}$-limit points and
$\mathcal{I}$-Cluster points of functions defined on
discrete countable amenable groups. Finally, we introduce and
investigate $\mathcal{I}$-limit superior and
$\mathcal{I}$-limit inferior of functions defined on
discrete countable amenable groups.