Best Proximity Point Results in Graphical Metric Space and Application

This article introduces and investigates the notion of ( Ψ , K )‐quasi graphical proximal contraction mappings within the framework of graphical metric spaces. We establish several best proximity point theorems for such mappings under appropriate structural and completeness assumptions. The obtained results are illustrated through suitable examples, demonstrating the validity and applicability of the theoretical framework. As an application, we derive some fixed point results as particular cases, thereby extending and unifying numerous existing results in the literature. Furthermore, we also explore the application of our theoretical findings to fractional integral equations, demonstrating the practical relevance of the proposed framework.