Abstract and Applied Analysis

Abstract and Applied Analysis / 2003 / Article

Open Access

Volume 2003 |Article ID 546707 | https://doi.org/10.1155/S1085337503209064

P. S. Srinivasan, P. Veeramani, "On best proximity pair theorems and fixed-point theorems", Abstract and Applied Analysis, vol. 2003, Article ID 546707, 15 pages, 2003. https://doi.org/10.1155/S1085337503209064

On best proximity pair theorems and fixed-point theorems

Received27 Nov 2001

Abstract

The significance of fixed-point theory stems from the fact that it furnishes a unified approach and constitutes an important tool in solving equations which are not necessarily linear. On the other hand, if the fixed-point equation Tx=x does not possess a solution, it is contemplated to resolve a problem of finding an element x such that x is in proximity to Tx in some sense. Best proximity pair theorems analyze the conditions under which the optimization problem, namely minxAd(x,Tx) has a solution. In this paper, we discuss the difference between best approximation theorems and best proximity pair theorems. We also discuss an application of a best proximity pair theorem to the theory of games.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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