Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2003, Number 1 (2003), 33-47.
On best proximity pair theorems and fixed-point theorems
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.
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
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