Recent results in the fixed point theory of continuous maps

Abstract

1. Introduction. Given a function/: X-+X, any question which inquires into the existence, nature and number of points xzX such that (#)=# is called fixed point theory. The assumptions on and X range from practically none (e.g., X is a set, a function) to quite stringent assumptions on and -X" (e.g., X is a Riemannian manifold and is an isometry). Our attention will be focused on results which require X to be a fairly reasonable space (e.g., a finite polyhedron) and a map ( = continuous function). Furthermore, we will limit our discussion to results which are not included in the expository tract [49] by Van der Walt (1967), which adequately covers the history of the subject from its beginning around 1910 to the early sixties.