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fixed points; multivalued contractions; absolute retracts
We establish a fixed point theorem for a continuous function $f:X\to E$, where $E$ is a Banach space and $X\subseteq E$. Our result, which involves multivalued contractions, contains the classical Schauder fixed point theorem as a special case. An application is presented.
[1] Aubin J.P., Frankowska H.: Set-Valued Analysis. Birkhäuser, Boston, 1990. MR 1048347 | Zbl 1168.49014
[2] Dugundji J., Granas A.: Fixed Point Theory. Vol. I, PWN - Polish Scientific Publishers, Warsaw, 1982. MR 0660439 | Zbl 1025.47002
[3] Hoffmann A.: The distance to the intersection of two convex sets expressed by the distances to each of them. Math. Nachr. 157 (1992), 81-98. MR 1233049 | Zbl 0773.52002
[4] Klein E., Thompson A.C.: Theory of Correspondences. John Wiley and Sons, New York, 1984. MR 0752692 | Zbl 0556.28012
[5] Ricceri B.: Une propriété topologique de l'ensemble des points fixes d'une contraction multivoque à valeurs convexes. Atti Acc. Lincei Rend. Fis. 81 (8) (1987), 283-286. MR 0999821 | Zbl 0666.47030
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