Fixed Point Theorems for Weakly Contractive Mappings in G-Metric Spaces

Abstract

This paper investigates the existence and uniqueness of fixed points for weakly contractive mappings in the context of G-metric spaces. We extend several classical fixed point theorems by introducing a new class of weakly contractive conditions that generalize the standard contractive inequalities. Our main results establish sufficient conditions for the existence of fixed points under various weak contraction principles, including φ-weak contractions and generalized Ćirić-type mappings. Furthermore, we provide examples to demonstrate that our results properly extend the existing literature, and we discuss applications to nonlinear integral equations. The presented theorems not only complement the current body of knowledge on fixed point theory in G-metric spaces but also open avenues for future research in related areas.