Generalized ideal convergence in intuitionistic fuzzy normed linear spaces

An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. In [19], Kostyrko et al. introduced the concept of ideal convergence as a sequence (xk) of real numbers is said to be I-convergent to a real number l, if for each ε > 0...

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Bibliographic Details
Published in:Filomat 2013-01, Vol.27 (5), p.811-820
Main Authors: Hazarika, Bipan, Kumar, Vijay, Lafuerza-Guillén, Bernardo
Format: Article
Language:English
Subjects:
College mathematics
Fuzzy set theory
Mathematical intuitionism
Mathematical sequences
Mathematical set theory
Real numbers
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Summary:An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. In [19], Kostyrko et al. introduced the concept of ideal convergence as a sequence (xk) of real numbers is said to be I-convergent to a real number l, if for each ε > 0 the set {k ∈ N : |xk− l| ≥ ε} belongs to I. The aim of this paper is to introduce and study the notion of λ-ideal convergence in intuitionistic fuzzy normed spaces as a variant of the notion of ideal convergence. Also Iλ−limit points and Iλ-cluster points have been defined and the relation between them has been established. Furthermore, Cauchy and Iλ-Cauchy sequences are introduced and studied.
ISSN:0354-5180
2406-0933
DOI:10.2298/FIL1305811H