Best Proximity Points: Optimal Solutions

Best Proximity Points: Optimal Solutions

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Article ID: iaor20119972
Volume: 151
Issue: 1
Start Page Number: 210
End Page Number: 216
Publication Date: Oct 2011
Journal: Journal of Optimization Theory and Applications
Authors:
Keywords: approximation, Banach space
Abstract:

This article elicits a best proximity point theorem for non‐self‐proximal contractions. As a consequence, it ascertains the existence of an optimal approximate solution to some equations for which it is plausible that there is no solution. Moreover, an algorithm is exhibited to determine such an optimal approximate solution designated as a best proximity point. It is interesting to observe that the preceding best proximity point theorem includes the famous Banach contraction principle.

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