Sehie Park

Copyright © 1997 Sehie Park. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let X be a Hausdorff compact space, E a topological vector space on which E* separates points, F:X→2E an upper semicontinuous multifunction with compact acyclic values, and g:X→E a continuous function such that g(X) is convex and g−1(y) is acyclic for each y∈g(X). Then either (1) there exists an x0∈X such that gx0∈Fx0 or (2) there exist an (x0,z0) on the graph of F and a continuous seminorm p on E such that 0<p(gx0−z0)≤p(y−z0)         for all         y∈g(X). A generalization of this result and its application to coincidence theorems are obtained. Our aim in this paper is to unify and improve almost fifty known theorems of others.