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    On ideal convergence of double sequences in probabilistic normed spaces

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    On Ideal Convergence of Double Sequences....pdf (227.1Kb)
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    URI: http://hdl.handle.net/10835/2754
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    Author/s
    Lafuerza Guillén, Bernardo; Kumar, Vijay
    Date
    2011-06-23
    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.
    Palabra/s clave
    Mathematics
    Probabilistic Normed Spaces
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    • Artículos de revista Dpto. Matemáticas [119]

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