A Study on Rough Ideal Statistical Convergence in Neutrosophic Normed Spaces

In this paper, we introduce and study the concept of rough I–αβ–statistical convergence of order γ in neutrosophic normed spaces. This new mode of convergence combines the principles of rough convergence, statistical convergence with respect to an ideal, and the flexible structure of neutrosophic norms to handle indeterminacy and vagueness in sequence behavior. We establish fundamental properties of this convergence type and investigate the structure of its limit set. Specifically, we prove that the set of rough I–αβ–statistical limit points of order γ is convex and closed under certain conditions. We further analyze the relationship between cluster points and rough statistical limits in this context. The theoretical results are supported by illustrative examples to demonstrate the validity and applicability of the proposed notions. Our findings generalize several existing convergence concepts and contribute to the growing body of research in neutrosophic functional analysis.