λ-ideal convergence in intuitionistic fuzzy 2-normed linear space

Authors:
Ayhan Esi;Bipan Hazarika
Affiliations:
Department of Mathematics, Science and Art Faculty, Adiyaman University, Adiyaman, Turkey;Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh, Arunachal Pradesh, India
Venue:
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Year:
2013

Citing 2
Cited 2

On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space

Journal of Computational and Applied Mathematics
On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces

Computers & Mathematics with Applications

On σ-uniform density and ideal convergent sequences of fuzzy real numbers

Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Some completeness results in terms of infinite series and quotient spaces in intuitionistic fuzzy n-normed linear spaces

Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology

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Abstract

An ideal I is a family of subsets of positive integers $\mathbb{N}$ 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 xk of real numbers is said to be I-convergent to a real number $\ell$, if for each ε 0 the set $\{k\in\mathbb{N}:|x_{k}-\ell|\geq\varepsilon\}$ 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 Iλ-limit points and Iλ-cluster points have been defined and the relation between them has been establish. Furthermore, Cauchy and Iλ-Cauchy sequences are introduced and studied.