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In this study, firstly, we studied some properties of $\mathcal{I}_2$-convergence. Then, we introduced $\mathcal{I}_2$-Cauchy and $\mathcal{I}_2^*$-Cauchy sequence of double sequences of functions in $2$-normed space. Also, were investigated relationships between them for double sequences of functions in $2$-normed spaces.

ON $\mathcal{I}_2$-CONVERGENCE AND $\mathcal{I}_2$-CAUCHY DOUBLE SEQUENCES OF FUNCTIONS IN 2-NORMED SPACES