Unique Common Fixed Point Theorems for Weakly Commuting Mapping in Complete 2-Metric Space

This paper develops fixed-point theorems in complete 2-metric spaces by extending the Banach contraction principle and establishes the existence of a common fixed point for commuting mappings. These results broaden the scope of fixed-point theory in generalized metric structures, offering valuable tools for mathematical analysis and diverse applications. The study enriches the theoretical foundation of nonlinear analysis while creating new opportunities for solving complex problems in applied mathematics. Its findings hold significance for optimization, computer science, and mathematical modeling, where generalized metrics frequently occur, and provide a strong basis for advancing both pure and applied research.