On $\mathcal{I}$-uniform convergence of sequences of functions in 2-normed spaces

Abstract

In this work, we discuss various kinds of $\mathcal{ℐ}$-uniform convergence for sequences of functions and introduce the concepts of ${\mathcal{ℐ}}^{\ast }$-uniform convergence, $\mathcal{ℐ}$ and ${\mathcal{ℐ}}^{\ast }$-uniformly Cauchy sequences of functions in $2$-normed spaces. Then, we show the relationships between them.