Existence of the solution to variational inequality, optimization problem, and elliptic boundary value problem through revisited best proximity point results

In this paper, we establish some results regarding the existence of the solution to variational inequality, optimization problem and elliptic boundary value problem in Hilbert spaces. Our strategy consists in establishing new best proximity point results in the metric spaces by introducing the concept of cyclic orbital simulative contractions. We also provide nontrivial examples to show that our results are proper generalization. Further, we improve the recent best proximity results for mappings satisfying proximal simulative conditions due to Abbas et al. (2017), Samet (2015), and Tchier et al. (2016) via new class of simulation functions. Our results unify, extend and generalize various existing results. (C) 2020 Elsevier B.V. All rights reserved.