Best proximity problems for new types of $\mathcal{Z}$-proximal contractions with an application

Abstract

In this study, we establish existence and uniqueness theorems of best proximity points for new types of $\mathcal{Z}$-proximal contractions defined on a complete metric space. The presented results improve and generalize some recent results in the literature. Several examples are constructed to demonstrate the generality of our results. As applications of the obtained results, we discuss sufficient conditions to ensure the existence of a unique solution for a variational inequality problem.

Keywords

• Best proximity point
• $ (\alpha\eta) $-admissible mapping
• $\mathcal{Z}$-contraction
• simulation function
• variational inequality

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