Fixed Point Theory and Applications
Volume 2004 (2004), Issue 4, Pages 317-336
On some Banach space constants arising in nonlinear fixed point
and eigenvalue theory
1Mathematisches Institut, Universität Würzburg,, Am Hubland, Würzburg 97074, Germany
2Department of Mathematics, Moscow State Institute of Electronic Techniques, Zelenograd, K-498, Moscow 124498, Russia
3Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira, Las Palmas de Gran Canaria 35017, Spain
Received 8 June 2004
Copyright © 2004 Jürgen Appell et al. 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.
As is well known, in any infinite-dimensional Banach space one
may find fixed point free self-maps of the unit ball, retractions
of the unit ball onto its boundary, contractions of the unit
sphere, and nonzero maps without positive eigenvalues and
normalized eigenvectors. In this paper, we give upper and lower
estimates, or even explicit formulas, for the minimal Lipschitz
constant and measure of noncompactness of such maps.