Fixed Point Theory and Applications
Volume 2006 (2006), Issue 3, Pages 36361, 30 p.
doi:10.1155/FPTA/2006/36361

Merging of degree and index theory

Abstract

The topological approaches to find solutions of a coincidence equation f1(x)=f2(x) can roughly be divided into degree and index theories. We describe how these methods can be combined. We are led to a concept of an extended degree theory for function triples which turns out to be natural in many respects. In particular, this approach is useful to find solutions of inclusion problems F(x)∈Φ(x). As a side result, we obtain a necessary condition for a compact AR to be a topological group.