P. S. Srinivasan, P. Veeramani, "On best proximity pair theorems and fixed-point theorems", Abstract and Applied Analysis, vol. 2003, Article ID 546707, 15 pages, 2003. https://doi.org/10.1155/S1085337503209064
On best proximity pair theorems and fixed-point theorems
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 does not possess a solution, it is contemplated to resolve a problem of finding an element such that is in proximity to in some sense. Best proximity pair theorems analyze the conditions under which the optimization problem, namely 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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