International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 4, Pages 689-698
Extensions of best approximation and coincidence theorems
Department of Mathematics, Seoul National University, Seoul 151–742, Korea
Received 15 December 1995
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.
Let be a Hausdorff compact space, a topological vector space on which separates points, an upper semicontinuous multifunction with compact acyclic
values, and a continuous function such that is convex and is acyclic for
each . Then either (1) there exists an such that or (2) there exist an on the graph of and a continuous seminorm on such that . 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.