On Weak Compatible Mappings, 3-D Column Graphs Approach in Multiplicative Generalized Metric Spaces With an Application

The purpose of this work is to investigate the approach to 3-D column graphs in multiplicative generalized metric spaces (MGM-spaces) utilizing single-valued mappings with an application. In MGM-space, we use weakly compatible four self-mappings to prove common fixed point (CFP) results without requiring their continuity. To support our findings, we provide nontrivial illustrative examples of CFP in MGM-spaces. In addition, we create 3-D column graphs to validate the contraction conditions of four self-mappings in MGM-spaces. Furthermore, we apply the nonlinear integral equation (NIE) to determine the existence of a unique common solution to unify our CFP results in the said domain. Our hypothesis will be critical to the theory of fixed points. Our findings can be expanded and improved in various ways by employing multiple sorts of mappings in MGM-spaces with applications.