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.
On some Banach space constants arising in nonlinear fixed point and eigenvalue theory
1 Mathematisches Institut, Universität Würzburg, Am Hubland, Würzburg 97074, Germany
2 Department of Mathematics, Moscow State Institute of Electronic Techniques, Zelenograd, K-498, Moscow 124498, Russia
3 Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira, Las Palmas de Gran Canaria 35017, Spain
Fixed Point Theory and Applications 2004, 2004:719153 doi:10.1155/S1687182004406068
The electronic version of this article is the complete one and can be found online at: http://www.fixedpointtheoryandapplications.com/content/2004/4/719153
|Received:||8 June 2004|
|Published:||26 December 2004|
© 2004 Appell et al.