On I -lacunary statistical convergence of weight g of fuzzy numbers

Abstract

In this paper, following a very recent and new approach of [1], we discuss a relation between two kinds of$\mathcal{I}$- convergence of sequences, namely, $\mathcal{I}$-statistical convergence of weight g and $\mathcal{I}$-lacunary statistical convergence of weight g, where $g:\mathbb{N}\to [0,\infty )$ is a function satisfying $\underset{n\to \infty }{lim}g\left(n\right)=\infty$ and $\frac{n}{g\left(n\right)}\nrightarrow 0$ as n→ ∞ for fuzzy numbers. These methods are based on the methods of statistical convergence and lacunary statistical summability for sequences. Analogs of inclusion and consistency theorems for the sequential methods are established.