On ideal convergence of double sequences in probabilistic normed spaces

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• 作者：Vijay Kumar (1) vjy_kaushik@yahoo.com
  Bernardo Lafuerza-Guillén (2) blafuerz@ual.es
• 关键词：Ideal convergence – double sequence – statistical convergence – continuous t ; norm and probabilistic normed spaces
• 刊名：Acta Mathematica Sinica
• 出版年：2012
• 出版时间：August 2012
• 年：2012
• 卷：28
• 期：8
• 页码：1689-1700
• 全文大小：233.5 KB
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• 作者单位：1. Department of Mathematics, Haryana College of Technology and Management, Kaithal, 136027 Haryana, India2. Departamento de Estadística y Matemática Aplicada, Universidad de Almería, Almería, 04120 Spain
• ISSN：1439-7617

文摘

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.