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

Jürgen Appell,1 Nina A. Erzakova,2 Sergio Falcon Santana,3 and Martin Väth1

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.