Handbook of Topological Fixed Point Theory

Fixed point theory concerns itself with a very simple, and basic, mathematical setting. For a functionf that has a setX as bothdomain and range, a ?xed point off isa pointx ofX for whichf(x)=x. Two fundamental theorems concerning ?xed points are those of Banach and of Brouwer. In Banach s theorem, X is a complete metric space with metricd andf: X?X is required to be a contraction, that is, there must existL