On power series strong and statistical convergences for double sequences via Orlicz functions

The present paper introduces the notions of strong P p 2 {P_{p}<^>{2}} -convergence and P p 2 {P_{p}<^>{2}} -statistical convergence for double sequences with respect to an Orlicz function. Based on these new notions of convergence, new double sequence spaces and some of their properties are given. Furthermore, certain inclusion relations are analyzed. Finally, we observe that, under proper choices, the analogous results can be obtained for modulus function.