ON IDEAL CONVERGENCE OF DOUBLE SEQUENCES IN NEUTROSOPHIC FUZZY G-METRIC SPACES

Abstract

The primary aim of this article is to introduce the concept of ideal convergence for double sequences in neutrosophic fuzzy G-metric spaces (NFGMS) with order q. We explore the fundamental properties of this concept, analyze I<inf>2</inf>-Cauchy double sequences, and examine I<inf>2</inf> completeness in NFGMS. We provide examples of ideal convergent NFGMS and discuss their algebraic and topological properties. Additionally, we investigate the I<inf>2</inf>-limit and I<inf>2</inf>-cluster points of sequences. We also present I<inf>2</inf>-statistical convergence, I<inf>2</inf>-lacunary statistical convergence, strong I<inf>2</inf>-Cesàro summability, and strong I<inf>2</inf>-lacunary summability with order q in NFGMS, along with their associated properties. © 2025 Elsevier B.V., All rights reserved.