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

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 epsilon > 0 the set {k is an element of N : vertical bar x(k) - l vertical bar >= epsilon} belongs to I. The aim of this paper is to introduce and study the notion of lambda-ideal convergence in intuitionistic fuzzy 2-normed space as a variant of the notion of ideal convergence. Also I-lambda-limit points and I-lambda-cluster points have been defined and the relation between them has been established. Furthermore, Cauchy and I-lambda-Cauchy sequences are introduced and studied.