On Best Proximity Points under the P -Property on Partially Ordered Metric Spaces

Abstract

Very recently, Abkar and Gabeleh (2013) observed that some best proximity point results under the $P$-property can be obtained from the same results in fixed-point theory. In this paper, motivated by this mentioned work, we show that the most best proximity point results on a metric space endowed with a partial order (under the $P$-property) can be deduced from existing fixed-point theorems in the literature. We present various model examples to illustrate this point of view.