NONLINEAR CONVERGENCE DYNAMICS IN FUZZY METRIC SPACES WITH APPLICATIONS TO DECISION-MAKING AND IMAGE PROCESSING

ROSHNI  SAHU; RAM MILAN  SINGH; MANOJ KUMAR  SHUKLA

ROSHNI SAHU DEPARTMENT OF MATHEMATICS, INSTITUTE FOR EXCELLENCE IN HIGHER EDUCATION, BHOPAL, INDIA
RAM MILAN SINGH DEPARTMENT OF MATHEMATICS, INSTITUTE FOR EXCELLENCE IN HIGHER EDUCATION, BHOPAL, INDIA
MANOJ KUMAR SHUKLA DEPARTMENT OF MATHEMATICS, BHABHA UNIVERSITY, BHOPAL, INDIA

Keywords: Fixed points, fuzzy metric spaces, nonlinear iterations, multi-valued mappings, decision-making, image processing, stability analysis.

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.

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