$\mathcal{I}_2$-Uniform Convergence of Double Sequences of Functions In $2$-Normed Spaces

Year 2022, Volume 5, Issue 3, 150 - 160, 30.09.2022

Sevim YEGÜL GÜZEY Erdinç DÜNDAR Mukaddes ARSLAN

https://doi.org/10.33434/cams.1177174

Abstract

In this work, we discuss various types of $\mathcal{I}_2$-uniform convergence and equi-continuous for double sequences of functions. Also, we introduce the concepts of $\mathcal{I}_2$-uniform convergence, $\mathcal{I}_2^*$-uniform convergence, $\mathcal{I}_2$-uniformly Cauchy sequences and $\mathcal{I}_2^*$-uniformly Cauchy sequences for double sequences of functions in $2$-normed spaces. Then, we show the relationships between these new concepts.

Keywords

Double sequence of functions, $\mathcal{I}$-Convergence, Uniformly convergence, 2-normed spaces

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