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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]

In this paper, we employ two types of implicit relations to define some new kind of proximal contractions and study about their best proximity points. More precisely, we use two class of functions A and A' to explore proximal A, A'-contractions of first and second kind and strong proximal A, A'-contractions. We investigate the existence of best proximity points results of the same. It is worth mentioning that the well-known results of Sadiq Basha [J. Approx. Theory, 2011] on proximal contractions are the special cases of our obtained results. We authenticate our results by suitable examples. Finally, we point out some areas where our obtained results can be applied. [ABSTRACT FROM AUTHOR]

Let us consider a non-self mapping T : A → B, where A and B are two nonempty subsets of a metric space (X,d). The aim of this paper is to solve the nonlinear programming problem that consists in minimizing the real valued function x → d(x,T x), where T belongs to a new class of non-self mappings. In especial case, existence and uniqueness of fixed point for Kannan type self mappings are also obtained. [ABSTRACT FROM AUTHOR]