On ideal convergence of double sequences in probabilistic normed spaces

Abstract

The notion of ideal convergence is a generalization of statistical convergence wich has been intensively investigated in last few years. For an admisible ideal f in NxN, the aim of the present paper is to introduce the concepts of f-convergence and f^*-convergence for double sequences on probabilistic normed spaces (PN spaces for short). We give some relations related to these notions and find conditions on the ideal f for which both the notions coincide. We also define f-Cauchy and f^*-Cauchy double sequences on PN spaces and show that f-convergent double sequences are f-Cauchy on these spaces. We establish example which shows that our method of convergence for double sequences on PN spaces is more general.