Generalized Ideal Convergence in Intuitionistic Fuzzy Normed Linear Spaces

Bipan Hazarika, Vijay Kumar, Bernardo Lafuerza-Guillén

An ideal $I$ is a family of subsets of positive integers $Bbb N$ 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 $x_k$ of real numbers is said to be $I$-convergent to a real number $\ell$, if for each $\varepsilon >0$ the set $\{k\in \Bbb N:|x_k-\ell|\geq \varepsilon\}$ belongs to $I$. The aim of this paper is to introduce and study the notion of $\lambda$-ideal convergence in intuitionistic fuzzy normed spaces 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.