Given a non-self mapping from A to B, where A and B are subsets of a metric space, in order to compute an optimal approximate solution of the equation S x = x , a best proximity point theorem probes into the global minimization of the error function x ? d ( x , S x ) corresponding to approximate solutions of the equation S x = x . This paper presents a best proximity point theorem for generalized contractions, thereby furnishing optimal approximate solutions, called best proximity points, to some non-linear equations. Also, an iterative algorithm is presented to compute such optimal approximate solutions. MSC:90C26, 90C30, 41A65, 46B20, 47H10, 54H25.
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机译：给定从A到B的非自我映射，其中A和B是度量空间的子集，为了计算方程S x = x的最佳近似解，最佳接近点定理将探索A的全局最小化。误差函数x？ d（x，S x）对应于方程S x = x的近似解。本文提出了广义收缩的最佳邻近点定理，从而为某些非线性方程提供了最佳近似解，称为最佳邻近点。此外，提出了一种迭代算法来计算这种最佳近似解。 MSC：90C26、90C30、41A65、46B20、47H10、54H25。
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