Let and be nonempty subsets of a metric space and also and , . We are going to consider element such that for some . We call pair an approximate best proximity pair. In this paper, definitions of approximate best proximity pair for a map and two maps, their diameters, -minimizing a sequence are given in a metric space.
S. A. M. Mohsenalhosseini. H. Mazaheri. M. A. Dehghan. "Approximate Best Proximity Pairs in Metric Space." Abstr. Appl. Anal. 2011 1 - 9, 2011. https://doi.org/10.1155/2011/596971