On best proximity pair theorems and fixed-point theorems
2003 ◽
Vol 2003
(1)
◽
pp. 33-47
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Keyword(s):
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 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 best approximation theorems and best proximity pair theorems. We also discuss an application of a best proximity pair theorem to the theory of games.
2005 ◽
Vol 2005
(5)
◽
pp. 789-801
Keyword(s):
2019 ◽
Vol 8
(10S)
◽
pp. 85-89
Keyword(s):
2012 ◽
Vol 2012
(1)
◽
pp. 103
◽
Keyword(s):
2002 ◽
Vol 30
(10)
◽
pp. 627-635
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Keyword(s):