On ideal convergence of double sequences in probabilistic normed spaces
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 probabilist...
| Main Authors: | , |
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
| Published: |
Acta Mathematica Sinica, English Series
2014
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10835/2754 |
| Summary: | 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. |
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