Contractive Conditions for Fixed Points in Complete Neutrosophic Fuzzy Metric Spaces

Fixed point theory constitutes a fundamental pillar of nonlinear analysis and has found extensive applications in mathematical modeling, optimization, computer science, and engineering. Classical results such as Banach's contraction principle have been generalized to various settings, including fuzzy metric spaces, cone metric spaces, and modular metric spaces. However, these frameworks often prove inadequate for modeling uncertainty involving indeterminacy and inconsistency. To address this limitation, neutrosophic fuzzy metric spaces (NFMSs) provide a powerful mathematical structure by integrating fuzzy distance measures with neutrosophic logic. In this paper, we establish several new fixed point theorems for single-valued mappings in complete neutrosophic fuzzy metric spaces under different generalized contractive conditions. The proposed contractions extend classical Banach-type, nonlinear, and rational-type contractions by incorporating neutrosophic fuzzy control functions. Using iterative techniques and properties of t-norms, we prove the existence and uniqueness of fixed points and demonstrate the convergence of the associated Picard iterative sequences. The obtained results significantly generalize and unify several existing fixed point theorems in fuzzy metric spaces, cone metric spaces, and modular metric spaces. An illustrative example is provided to validate the applicability of the main results. The primary contribution of this work lies in enriching the theoretical foundation of neutrosophic fuzzy analysis and offering a unified approach to handling uncertainty, vagueness, and inconsistency within fixed point theory. Although this study is mainly theoretical, the results have potential implications for optimization theory, decision-making models, and computational intelligence systems operating under indeterminate or conflicting information. Future research may focus on extending these results to multivalued mappings and their applications in real-world neutrosophic models.