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

Authors : Sevim YEGÜL GÜZEY, Erdinç DÜNDAR, Mukaddes ARSLAN

Pages : 150-160

Doi:10.33434/cams.1177174

View : 14 | Download : 10

Publication Date : 2022-09-30

Article Type : Research Paper

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