(untitled) (European Journal of Pure and Applied Mathematics, 2025)
This work presents the notion of complex-valued neutrosophic metric spaces (CVNMSs) and provides a fresh mathematical framework extending conventional fuzzy and intuitionistic fuzzy metric spaces (IFMSs). This new method is especially appropriate for studying complicated mathematical structures since it helps to better depict uncertainty and imprecision by including neutrosophic sets. We determine the existence and uniqueness of fixed points under several contractive mappings in this newly defined metric space. Our results extend the classical Banach contraction ideas and modify them for the neutrosophic environment. We demonstrate several fixed-point theorems, expanding the applicability of current fixed-point results in non-classical metric spaces. We use our results to solve Fredholm integral equations and show the efficiency of CVNMSs in tackling real-world mathematical problems by illustrating the pragmatic relevance of our results. Furthermore, comprehensive cases are included to show the relevance of our findings. This work also extends the fixed-point theory in neutrosophic environments and provides fresh directions for investigation in integral equations and contractive mappings.