NONLINEAR CONVERGENCE DYNAMICS IN FUZZYMETRIC SPACES WITH APPLICATIONS TODECISION-MAKING AND IMAGE PROCESSING

Abstract

This paper examines nonlinear convergence dynamics in fuzzy metric spaces, a framework that incorporates uncertainty into distance measures. We propose a nonlinear iterative scheme with adaptive parameters to establish the existence and uniqueness of fixed points under generalized contractive conditions. Our contributions include four novel theorems, substantiated by meticulous proofs and illustrated with colorful TikZ diagrams, addressing both single and multi-valued mappings. These findings are applied to multi-criteria decision-making, image segmentation, and stability in uncertain systems, highlighting their practical utility.