Pertubations compactes des contractions multivoques

LetE be a Banach space, θ a multivalued contraction with closed values onE andf a continuous function fromE to itself with conditionally compact range. We prove that multifunction ψ=f+θ has fixed points if θ is convex-valued or if the range off is contained in a Lipschitz simple path. We also prove by counterexamples that the previous result is not true if the range off is only assumed to be homeomorphic to a segment or diffeomorphic to a circle.