Lacunary ideal convergence of multiple sequences in probabilistic normed spaces

Bipan Hazarika

Applied Mathematics and Computation, 2016, vol. 279, issue C, 139-153

Abstract: An ideal I is a family of subsets of positive integers N×N which is closed under finite unions and subsets of its elements. The aim of this paper is to study the notion of lacunary I-convergence of double sequences in probabilistic normed spaces as a variant of the notion of ideal convergence. Also lacunary I-limit points and lacunary I-cluster points have been defined and the relation between them has been established. Furthermore, lacunary-Cauchy and lacunary I-Cauchy, lacunary I*-Cauchy, lacunary I*-convergent double sequences are introduced and studied in probabilistic normed spaces. Finally, we provided example which shows that our method of convergence in probabilistic normed space is more general.

Keywords: Ideal convergence; Double sequence; Probabilistic normed space; Double lacunary sequence; θ-convergence (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:279:y:2016:i:c:p:139-153

DOI: 10.1016/j.amc.2015.12.048

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