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