Abstract
In this article, we establish new best proximity point theorems for cyclic contraction mappings as well as for cyclic relatively nonexpansive mappings under different sufficient conditions. We give some examples to support our main conclusions. We also prove some common best proximity point theorems for a commuting family of cyclic relatively nonexpansive mappings. As applications of the existence theorems, we extend DeMarr's theorem and the results of Belluce and Kirk [L.P. Belluce and W.A. Kirk, Fixed point theorems for families of contraction mappings, Pacific J. Math., 18 (1966) 213-217] for best proximity points.