Abstract and Applied Analysis

On best proximity pair theorems and fixed-point theorems

P. S. Srinivasan and P. Veeramani

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 15 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1050426083

Digital Object Identifier
doi:10.1155/S1085337503209064

Mathematical Reviews number (MathSciNet)
MR1954244

Zentralblatt MATH identifier
1023.47035

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

Citation

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


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