Generalized difference statistical convergence of order α in Neutrosophic n-Normed linear spaces: New perspectives in the ideal setting

Abstract

In this paper, we introduce and investigate novel notions of generalized difference statistical convergence of order alpha(0<= 1) within the framework of neutrosophic n-normed linear spaces. We develop and analyze the concepts of generalized difference statistical convergence, lacunary statistical convergence, and lacunary convergence of order alpha via ideals. A significant result shows that strongly J-Delta(m)-lacunary convergence of order alpha implies J-Delta(m)-lacunary statistical convergence of the same order, although the converse does not hold in general. However, this converse implication becomes true when alpha=1 and the sequence in question is Delta(m)-bounded. We further explore the inclusion relationships between generalized difference statistical convergence and lacunary statistical convergence of order alpha with respect to ideals in the neutrosophic n-normed context. Under the condition 0<=beta <= 1, we establish hierarchical inclusion results for the set of all generalized difference J-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 n-normed linear spaces.