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# Fuzzy real valued lacunary I-convergent sequences.

Applied Mathematics Letters (Impact Factor: 1.48). 03/2012; 25:466-470. DOI: 10.1016/j.aml.2011.09.037

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**ABSTRACT:**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 [8], Kostyrko et al., introduced the concept of ideal convergence as a sequence (x k ) of real numbers is said to be I-convergent to a real number ℓ, if for each ε>0 the set {k∈ℕ:|x k -ℓ|≥ε} belongs to I. The aim of this paper is to introduce and study the notion of λ-ideal convergence in intuitionistic fuzzy 2-normed space as a variant of the notion of ideal convergence. Also I λ -limit points and I λ -cluster points have been defined and the relation between them has been establish. Furthermore, Cauchy and I λ -Cauchy sequences are introduced and studied.Journal of Intelligent and Fuzzy Systems 07/2013; 24(4):725-732. · 0.94 Impact Factor - 11/2013;
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**ABSTRACT:**An ideal ℐ is a family of subsets of positive integers ℕ×ℕ which is closed under taking finite unions and subsets of its elements. In this paper, we present some definitions which are a natural combination of the definition of asymptotic equivalence, statistical convergence, lacunary statistical convergence, double sequences and an ideal. In addition, we also present asymptotically ℐ-equivalent double sequences and study some properties of this concept.Journal of Inequalities and Applications 01/2013; 2013. · 0.77 Impact Factor

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