Generalized Difference Statistical Convergence of Order α in Neutrosophic n -Normed Linear Spaces: New Perspectives in the Ideal Setting

In this paper, we introduce and investigate novel notions of generalized difference statistical convergence of order [Formula: see text] ([Formula: see text]) within the framework of neutrosophic [Formula: see text]-normed linear spaces. We develop and analyze the concepts of generalized difference statistical convergence, lacunary statistical convergence, and lacunary convergence of order [Formula: see text] via ideals. A significant result shows that strongly [Formula: see text]-[Formula: see text]-lacunary convergence of order [Formula: see text] implies [Formula: see text]-[Formula: see text]-lacunary statistical convergence of the same order, although the converse does not hold in general. However, this converse implication becomes true when [Formula: see text] and the sequence in question is [Formula: see text]-bounded. We further explore the inclusion relationships between generalized difference statistical convergence and lacunary statistical convergence of order [Formula: see text] with respect to ideals in the neutrosophic [Formula: see text]-normed context. Under the condition [Formula: see text], we establish hierarchical inclusion results for the set of all generalized difference [Formula: see text]-lacunary statistically convergent sequences. Additionally, we present further results on these sets based on a newly defined lacunary sequence satisfying the same order constraints. Some intriguing scenarios remain unresolved, and we conclude by posing these as open problems for future research within neutrosophic [Formula: see text]-normed linear spaces.