Best proximity point theorems for reckoning optimal approximate solutions
نویسنده
چکیده
*Correspondence: [email protected] 2Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Full list of author information is available at the end of the article Abstract 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 Sx = x, a best proximity point theorem probes into the global minimization of the error function x –→ d(x, Sx) corresponding to approximate solutions of the equation Sx = 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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