Tauberian Theorems and Statistical Cesàro Summability in the Framework of Neutrosophic Normed Spaces

Abstract

This paper establishes Tauberian theorems for statistical Cesàro summability in neutrosophic normed spaces. We prove that $q$-bounded sequences statistically convergent under the neutrosophic norm $(\mathfrak{A},\mathfrak{B},\mathfrak{C})$ are also statistically Cesàro summable, and characterize when the converse holds. Key results include a neutrosophic statistical slow oscillation condition and the role of $\{n(\upsilon_n - \upsilon_{n-1})\}$'s $q$-boundedness in ensuring statistical convergence.