On existence of best proximity pair theorems for relatively nonexpansive mappings

In this paper we study the existence of best proximity pair of points for relatively nonexpansive mappings on a pair A;B of subsets of a Banach space X. A recent paper by Espínola (A new approach to relatively nonexpansive mappings, Proc. Amer. Math. Soc. 136 (2008), no. 6, 1987-1995) contains best proximity pair theorems for relatively nonexpansive mappings on a proximial parallel pair in X. In this paper we obtain similar results for a more general class of pairs.