On best proximity pair theorems and fixed-point theorems

P. S. Srinivasan and P. Veeramani

Abstract and Applied Analysis, 2003, vol. 2003, 1-15

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 T x = 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 T x in some sense. Best proximity pair theorems analyze the conditions under which the optimization problem, namely min x ∈ A d ( x , T x ) 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.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:546707

DOI: 10.1155/S1085337503209064

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