Open Access

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

  • Jürgen Appell1Email author,
  • Nina A Erzakova2,
  • Sergio Falcon Santana3 and
  • Martin Väth1
Fixed Point Theory and Applications20042004:719153

DOI: 10.1155/S1687182004406068

Received: 8 June 2004

Published: 26 December 2004

Abstract

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.

Authors’ Affiliations

(1)
Mathematisches Institut, Universität Würzburg, Am Hubland
(2)
Department of Mathematics, Moscow State Institute of Electronic Techniques
(3)
Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria

Copyright

© Appell et al. 2004