Summary: We study the convergence of best proximity points for cyclic relatively nonexpansive mappings in the setting of uniformly convex Banach spaces by using a projection operator defined on proximal pairs. To this end, we consider the Mann and Ishikawa iteration schemes and obtain strong convergence results for cyclic relatively nonexpansive mappings. A numerical example is presented to support the main result. We then discuss on noncyclic version of relatively nonexpansive mappings in order to study some convergence conclusions in both uniformly convex Banach spaces and Hilbert spaces.