Une propriété topologique de l'ensemble des points fixes d'une contraction multivoque à valeurs convexes
Biagio Ricceri (1987)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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In this Note we first establish a result on the structure of the set of fixed points of a multi-valued contraction with convex values. As a consequence of this result, we then obtain the following theorem: Let , be two real Banach spaces and let be a continuous linear operator from onto . Put: . Then, for every and every lipschitzian operator , with Lipschitz constant such that , the set is non-empty and arc wise connected.