FIXED POINT THEOREMS IN COMPLETE FUZZY TWO-METRIC SPACES

Abstract

The concept of fixed points in mathematics, crucial for analysis and applications, gains new dimensions in the context of fuzzy 2-metric spaces. This study investigates the existence and uniqueness of fixed points for composite operators in these spaces, where uncertainty and fuzziness are integral. Leveraging Banach's Fixed Point Theorem, the research establishes conditions for mappings ????:????→???? and ????:????→???? to exhibit contractiveness, ensuring unique fixed points for compositions ???????? and ????????. Extending classical fixed-point theory, the study incorporates weighted inequalities and multidimensional metrics, enhancing its applicability to uncertain environments. Methodologically, sequences are iteratively analyzed within fuzzy metrics to prove convergence to unique fixed points, interlinked by the mappings. These results not only broaden theoretical frameworks but also provide practical tools for optimization, control theory, and fuzzy system modeling, addressing real-world challenges characterized by imprecision and vagueness.