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On ideal convergence of double sequences in probabilistic normed spaces

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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.

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Authors and Affiliations

  1. Department of Mathematics, Haryana College of Technology and Management, Kaithal, 136027, Haryana, India

    Vijay Kumar

  2. Departamento de Estadística y Matemática Aplicada, Universidad de Almería, Almería, 04120, Spain

    Bernardo Lafuerza-Guillén

Authors
  1. Vijay Kumar
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  2. Bernardo Lafuerza-Guillén
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Correspondence to Vijay Kumar.

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Kumar, V., Lafuerza-Guillén, B. On ideal convergence of double sequences in probabilistic normed spaces. Acta. Math. Sin.-English Ser. 28, 1689–1700 (2012). https://doi.org/10.1007/s10114-012-9321-1

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  • DOI: https://doi.org/10.1007/s10114-012-9321-1

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