Some Fixed Point Results on G-(E.A.) Property of Integral Type Mappings in G-Metric Spaces

This paper investigates the existence and uniqueness of fixed points for Lebesgue integrable self-mappings satisfying integral type contractive conditions in the framework of G-metric spaces. By employing the G-(E.A.) property together with weak compatibility, we establish fixed point results under weaker and more flexible assumptions, completely eliminating the need for continuity of the involved mappings. The obtained existence and uniqueness theorems unify and generalize several well-known fixed point results in metric, b-metric, and G-metric spaces. Furthermore, the fixed point problem is shown to be well posed. An illustrative example is provided to demonstrate the applicability of the main results. These findings contribute to a stronger theoretical foundation for further research in nonlinear analysis and related applications.