A Study of Fixed Point Results in G-Metric Space via New Contractions with Applications

In this manuscript, some novel classes of (G- \(\alpha \) - \(\phi )\) -contractions are introduced in the framework of generalized metric space and related fixed point results are obtained, which do not collapse to similar ones in metric spaces. These classes of mappings are dominant in the sense that they subsume a few known results in the literature. A comparative example is presented to verify the claims of the main results obtained and to differentiate them from the existing ones. Thereafter, a few special cases which scale down our results to some prominent ones in the literature are highlighted and analyzed. As an application, our main result is used to construct new existence criteria for the solution of a boundary value problem.