Abed Al-Rahman Malkawi, Ayat Rabaiah
In this paper, we introduce and study the concept of Neutrosophic MR-Metric Spaces (NMR-MS), which combine the structure of MR-metric spaces with neutrosophic membership functions. We establish a fixed point theorem for neutrosophic contraction mappings in such spaces and prove the existence, uniqueness, and measure-theoretic convergence of the fixed point. Our results extend classical fixed point theory to a more general framework that incorporates uncertainty and vagueness, as modeled by neutrosophic logic. The convergence is shown to be exponential in measure and stable under the induced measure structure. Several illustrative examples and applications are provided to validate the theoretical findings and demonstrate their applicability in dynamical systems, optimization, and stability analysis under uncertainty.