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

Abstract The present paper introduces the notions of strong <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mi>P</m:mi> <m:mi>p</m:mi> <m:mn>2</m:mn> </m:msubsup> </m:math> {P_{p}^{2}} -convergence and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mi>P</m:mi> <m:mi>p</m:mi> <m:mn>2</m:mn> </m:msubsup> </m:math> {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.