On best proximity pair theorems and fixed‐point theorems

P. S. Srinivasan and P. Veeramani

Abstract and Applied Analysis, 2003, vol. 2003, issue 1, 33-47

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 minx∈A d(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.

Date: 2003
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https://doi.org/10.1155/S1085337503209064

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2003:y:2003:i:1:p:33-47

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