the goal of this paper is to generalize the recently introduced summability method and introduce double statistical convergence of order  by using ideal. we also investigate certain properties of this convergence.

In this paper we extend the notion of rough convergence using the concept of ideals which automatically extends the earlier notions of rough convergence and rough statistical convergence. We define the set of rough ideal limit points and prove several results associated with this set.

in this paper, we introduce and study the concepts of $mathcal{i}_2$-convergence, $mathcal{i}_2^{*}$-convergence for double sequences of fuzzy real numbers, where $mathcal{i}_2$ denotes the ideal of subsets of $mathbb n times mathbb n$. also, we study some properties and relations of them.

We generalize the Bolzano-Weierstrass theorem (that every bounded sequence of reals admits a convergent subsequence) on ideal convergence. We show examples of ideals with and without the Bolzano-Weierstrass property, and give characterizations of BW property in terms of submeasures and extendability to a maximal P-ideal. We show applications to Rudin-Keisler and Rudin-Blass orderings of ideals ...