Abstract and Applied Analysis

On best proximity pair theorems and fixed-point theorems

P. S. Srinivasan and P. Veeramani

Full-text: Open access


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.

Article information

Abstr. Appl. Anal., Volume 2003, Number 1 (2003), 33-47.

First available in Project Euclid: 15 April 2003

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 47H04
Secondary: 54H25


Srinivasan, P. S.; Veeramani, P. On best proximity pair theorems and fixed-point theorems. Abstr. Appl. Anal. 2003 (2003), no. 1, 33--47. doi:10.1155/S1085337503209064. https://projecteuclid.org/euclid.aaa/1050426083

Export citation