Fixed Point Theory and Applications
Volume 2006 (2006), Article ID 29470, 10 pages
Epsilon Nielsen fixed point theory
Department of Mathematics, University of California, Los Angeles 90095-1555, CA, USA
Received 11 October 2004; Revised 17 May 2005; Accepted 21 July 2005
Copyright © 2006 Robert F. Brown. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a map of a compact, connected
Riemannian manifold, with or without boundary. For sufficiently small, we introduce an -Nielsen number that is a lower bound for the number of fixed
points of all self-maps of that are -homotopic to
. We prove that there is always a map that is -homotopic to such that has exactly fixed points. We describe procedures for
calculating for maps of -manifolds.