$ \nu- $Conull FDK-spaces

In this paper, we introduced the concepts of (strongly) $ \nu $-conull FDK-spaces, which can be regarded as double-indexed versions of FK-spaces (sequence space with coordinate functionals), by utilizing the notion of $ \nu $-convergence for double sequences. We provided fundamental characterizations of these new spaces and established several inclusion relations among them. Furthermore, we investigated the conditions under which the summability domain $ E_A^{(\nu)} $ is (strongly) $ \nu $-conull, thereby providing new insights into its structural and topological properties.