Abstract and Applied Analysis
Volume 2003 (2003), Issue 1, Pages 33-47

On best proximity pair theorems and fixed-point theorems

P. S. Srinivasan and P. Veeramani

Department of Mathematics, Indian Institute of Technology (IITM), Madras, Chennai 600 036, India

Received 27 November 2001

Copyright © 2003 P. S. Srinivasan and P. Veeramani. 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.


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.