Abstract
LetE be a Banach space,C a closed convex subset ofE, F a multivalued contraction fromC to itself with closed values. Ifx 0 is a fixed point and ifF(x 0) is not a singleton, then there exists a fixed pointx 1 ofF which is different fromx 0. We prove also that there is in the Euclidean space ℝ2 a multivalued contraction with compact connected values having a nonconnected set of fixed points.
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Saint Raymond, J. Multivalued contractions. Set-Valued Anal 2, 559–571 (1994). https://doi.org/10.1007/BF01033072
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DOI: https://doi.org/10.1007/BF01033072