A Fixed Point Theorem and Equivariant Points for Set-valued Mappings

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 Poincare space with a finite covering dimension, the covering dimension of the set of equivariant points is determined.