Analysis of Fixed Point Theorems for Contractive Mappings in Complex-Valued Neutrosophic Metric Spaces and Their Application

This paper introduces complex-valued neutrosophic metric spaces, extending the concepts of complex-valued fuzzy and intuitionistic fuzzy metric spaces. We establish the existence and uniqueness of fixed points for mappings under various contractive conditions within this framework. To improve clarity, we present illustrative examples. Furthermore, we demonstrate the applicability of our findings by proving the existence of a unique solution for Fredholm integral equations, emphasizing their practical relevance n mathe matical analysis and applied sciences.