Common Fixed Points of Compatible Mappings in G-Metric Type Spaces

This paper introduces and investigates the concept of compatible mappings in G-metric type spaces, establishing a novel framework for fixed point theory. We define and analyze the notion of compatibility between self-mappings in the context of G-metric type spaces, which generalizes existing compatibility conditions in metric spaces. Several fixed point theorems are proved by employing various contractive conditions on compatible mappings. Our main results extend and unify various theorems in the literature, demonstrating the efficacy of compatibility in obtaining common fixed points in G-metric type spaces. The theoretical significance of these findings is illustrated through examples and counterexamples, highlighting the necessity of our compatibility conditions.