$\mathcal I_2$-lacunary strongly summability for multidimensional measurable functions

Rabia Savaş, Richard F. Patterson

Let $\mathcal I_2\subseteq\mathcal P(\mathbb N\times\mathbb N)$ be a nontrivial ideal. We provide a new approach to the concept of $\mathcal I_2$-double lacunary statistical convergence and $\mathcal I_2$-lacunary strongly double summable by taking $f(\tau,\upsilon)$, which is a multidimensional measurable real valued function on $(1,\infty)\times(1,\infty)$. Additionally, we examine the relation between these two new methods.