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Open Access Research Article

On some Banach space constants arising in nonlinear fixed point and eigenvalue theory

Jürgen Appell1*, Nina A Erzakova2, Sergio Falcon Santana3 and Martin Väth1

Author Affiliations

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

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Fixed Point Theory and Applications 2004, 2004:719153  doi:10.1155/S1687182004406068

Published: 26 December 2004


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.