Open Access
16 January 2003 On best proximity pair theorems and fixed-point theorems
P. S. Srinivasan, P. Veeramani
Abstr. Appl. Anal. 2003(1): 33-47 (16 January 2003). DOI: 10.1155/S1085337503209064


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.


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P. S. Srinivasan. P. Veeramani. "On best proximity pair theorems and fixed-point theorems." Abstr. Appl. Anal. 2003 (1) 33 - 47, 16 January 2003.


Published: 16 January 2003
First available in Project Euclid: 15 April 2003

zbMATH: 1023.47035
MathSciNet: MR1954244
Digital Object Identifier: 10.1155/S1085337503209064

Primary: 47H04 , 47H10
Secondary: 54H25

Rights: Copyright © 2003 Hindawi

Vol.2003 • No. 1 • 16 January 2003
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