The Role of Lacimary Statistical Convergence for Double sequences in Neutrosophic Normed Spaces

This paper introduces and explores the concept of lacunary statistical convergence of double sequence within the framework neutrosophic normed spaces. Neutrosophic normed spaces extend classical normed spaces by incorporating neutrosophic numbers, which account for the inherent uncertainty, indeterminacy, and vagueness present in real - world data. The study begins by defining lacunary statistical convergence for double sequences in this extended context and proceeds to establish fundamental theorems and properties related to this new notion. In addition, we present a new idea in this context: statistical completeness. We demonstrate that, while neutrosophic normed space is statistically complete, it is not complete. Keywords: Neutrosophic Normed Spaces; Lacunary Statistical Convergence and Cauchyness; Statistical Completeness.