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In this note, at first we prove that the existence of best proximity pointsfor cyclic relatively nonexpansive mappings is equivalent to the existence ofbest proximity pairs for noncyclic relatively nonexpansive mappings in thesetting of strictly convex Banach spaces by using the projection operator. Inthis way, we conclude that a main result of the paper "Proximal normalstructure and relatively nonexpansive mappings", Studia Math., (171~(2005)283--293) immediately follows. We then discuss the convergence of bestproximity pairs for noncyclic contractions by applying the convergence ofiterative sequences for cyclic contractions and show that the convergencemethod of a recent paper published in Indag. Math., 30(1) (2019) 227--239 isobtained exactly from Picard's iteration sequence.

Some remarks on "Convergence of Picard's iteration using projection algorithm for noncyclic contractions" [Indag. Math. 30 (2019) 227--239]