Fixed Points of Expansion Type Maps

Abstract

In 1983 Gillespic and Williams showed that a continuous expansion of a finite dimensional Banach space has a fixed point. The present paper shows that a considerable relaxation of the expansion condition is possible so that, for example, the result becomes applicable to maps that are not necessarily injective. Topological difficulties occur in the proof which are resolved by use of the Borsuk-Ulam theorem.

Keywords:

• Fixed points
• expansion map
• finite dimension