On the lacunary $(A, ϕ)$ -statistical convergence of double sequences

Abstract

We extend some results known from the literature for ordinary (single) sequences to multiple sequences of real numbers. Further, we introduce a concept of double lacunary strong $(A, ϕ)$-convergence with respect to a modulus function. In addition, we also study some relationships between double lacunary strong $(A, ϕ)$-convergence with respect to a modulus and double lacunary statistical convergence.