Best proximity points for proximal Gornicki mappings and applications to variational inequality problems

We introduce a large class of mappings called proximal Gornicki mappings in metric spaces, which includes Gornicki mappings, enriched Kannan mappings, enriched Chatterjea mappings, and enriched mappings. We prove the existence of the best proximity points in metric spaces and partial metric spaces. Moreover, we utilize appropriate examples to illustrate our results, and we verify the convergence behavior. As an application of our result, we prove the existence and uniqueness of a solution for the variational inequality problems. The obtained results generalize the existing results in the literature.