Abstract and Applied Analysis
Volume 2003 (2003), Issue 1, Pages 33-47
On best proximity pair theorems and fixed-point theorems
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 does not possess a solution, it is contemplated to resolve a problem of finding an element such that is in proximity to in some sense. Best proximity pair theorems analyze the conditions under which the optimization problem, namely 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.