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Fixed Point Theory and Applications

, 2012:202

Professor Anthony To-Ming Lau-s contributions to the development of Fixed Point Theory and Applications.

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 S x = x Open image in new window, a best proximity point theorem probes into the global minimization of the error function x ⟶ d x , S x Open image in new window corresponding to approximate solutions of the equation S x = x Open image in new window. 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.

Keywordsglobal optimization optimal approximate solution best proximity point fixed point contraction generalized contraction non-expansive mapping  Download fulltext PDF



Author: S Sadiq Basha - N Shahzad - R Jeyaraj

Source: https://link.springer.com/



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