Best Proximity Points: Optimal Solutions


DOI: 10.1007/s10957-011-9869-4

Cite this article as:
Sadiq Basha, S. J Optim Theory Appl (2011) 151: 210. doi:10.1007/s10957-011-9869-4


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.


Optimal approximate solutionFixed pointBest proximity pointContractionProximal contraction

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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsAnna UniversityChennaiIndia