We give a proof of a coincidence theorem for a Vietoris mapping and a compact mapping and prove the Lefschetz fixed point theorem for the class of admissible mappings which contains upper semi-continuous acyclic mappings. When a source space is a paracompact Hausdorff space with a free involution and a target space is a closed topological manifold with an involution, the existence of equivariant points is proved for the class of admissible mappings under some conditions. When a source space is a Poincaré space with a finite covering dimension, the covering dimension of the set of equivariant points is determined.
Cite this article
Yoshimi Shitanda, A Fixed Point Theorem and Equivariant Points for Set-valued Mappings. Publ. Res. Inst. Math. Sci. 45 (2009), no. 3, pp. 811–844