Applications of Kakutani’s Theorem and its Extensions

Abstract

We now show how the ability to find approximate fixed points of upper semi-continuous mappings enables one to solve a wide range of important problems, without the limitations of Chapter II. Again we point out that constructing an appropriate mapping is relatively straightforward. Indeed, for any given problem it is easier than constructing a continuous function, since u.s.c. mappings can be patched together so easily.