On best proximity pair theorems and fixed-point theorems
Summary: 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 \(\min_{x\in A}d(x,Tx)\) 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.
scientific article; zbMATH DE number 1883733