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In this paper, we focus on the existence of the best proximity points in binormed linear spaces. As a consequence, we obtain some fixed point results. We also provide some illustrations to support our claims. As applications, we obtain the existence of a solution to split feasible and variational inequality problems. [ABSTRACT FROM AUTHOR]

There are situations when we have to resort to the approximate optimal solution of equations of the type g(t) = t when g is not a self-map, because exact solution of that equation does not exist. The existence of such optimal solutions are ensured by best proximity point theorems. In this paper, we define multivalued Geraghty contraction (MVGC) in a complete metric space and establish the corresponding best proximity point (BPP) result. Our result extends the famous result due to Geraghty on fixed points. [ABSTRACT FROM AUTHOR]

In this paper, we extend the result of Romaguera [21] with the aid of best proximity point theory on partial metric spaces by considering the approach of Haghi et al. [9], and so celebrated Boyd-Wong fixed point theorem [7]. We first introduce two concepts called generalized proximal BW-contraction and generalized best BW-contraction. Then, we obtain some best proximity point theorems for such mappings. To illustrate the effectiveness of our results, we provide some nontrivial and interesting examples. Finally, unlike homotopy applications existing in the literature, we present for the first time an application of the best proximity result to the homotopy theory. [ABSTRACT FROM AUTHOR]