1. Department of Mathematics, Haryana College of Technology and Management, Kaithal, 136027, Haryana, India 2. Departamento de Estadística y Matemática Aplicada, Universidad de Almería, Almería, 04120, Spain
Abstract:
The notion of ideal convergence is a generalization of statistical convergence which has been intensively investigated in last few years. For an admissible ideal ∮ ? ? × ?, 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.