On best proximity pair theorems and fixed-point theorems

[摘要] The significance of fixed-point theory stems from the fact that itfurnishes a unified approach and constitutes an important tool insolving equations which are not necessarily linear. On the otherhand, if the fixed-point equationTx=xdoes not possess a solution, it is contemplated to resolve a problem of finding an elementxsuch thatxis in proximity toTxin some sense. Best proximity pair theorems analyze the conditions under which the optimization problem, namelyminx∈A d(x,Tx)has a solution. In this paper, we discuss the difference between bestapproximation theorems and best proximity pair theorems. We also discuss an application of a best proximity pair theorem to the theory of games.

[学科分类] 数学（综合）