Λ-ideal Convergence in Intuitionistic Fuzzy 2-normed Linear Space

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 e > 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.