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We obtain the homotopic invariance for fixed points of set-valued contractions and nonexpansive mappings whose domain is a bounded nonexpansive retract and nonempty interior subset of a uniformly convex Banach space. This gives a partial answer to a problem posed by Sims, Xu and Yuan (2001) .doi:10.12988/ijma.2013.35118 fatcat:qahtxudwhze3xlwipucr3e6bme