Analyzing lacunary <inline-formula><tex-math id="M1">$ \Delta^{m} $</tex-math></inline-formula>-statistical convergence in neutrosophic normed spaces

This paper explores the notions of lacunary $ \Delta^m $-statistical convergence, lacunary $ \Delta^m $-statistical Cauchy sequences, and lacunary strongly $ \Delta^m $-convergence within the framework of neutrosophic normed linear spaces (NNLS). We establish the uniqueness of limit and certain algebraic properties of lacunary $ \Delta^m $-statistical convergence in NNLS, offering a rigorous foundation for these concepts. Additionally, we introduce the concept of strong Cesàro summability in NNLS and conduct an in-depth analysis of its properties. The connections between lacunary strong $ \Delta^m $-convergence and Cesàro summability are also examined, revealing significant interrelationships between these two convergence methods.