On some Banach space constants arising in nonlinear fixed point and eigenvalue theory
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 uppe...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2004-12-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://dx.doi.org/10.1155/S1687182004406068 |
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doaj-044505bc0e764e689308d9acaad92aba2020-11-24T21:18:37ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122004-12-012004431733610.1155/S1687182004406068On some Banach space constants arising in nonlinear fixed point and eigenvalue theoryMartin VäthSergio Falcon SantanaNina A. ErzakovaJürgen AppellAs 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.http://dx.doi.org/10.1155/S1687182004406068 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Martin Väth Sergio Falcon Santana Nina A. Erzakova Jürgen Appell |
| spellingShingle |
Martin Väth Sergio Falcon Santana Nina A. Erzakova Jürgen Appell On some Banach space constants arising in nonlinear fixed point and eigenvalue theory Fixed Point Theory and Applications |
| author_facet |
Martin Väth Sergio Falcon Santana Nina A. Erzakova Jürgen Appell |
| author_sort |
Martin Väth |
| title |
On some Banach space constants arising in nonlinear fixed point and eigenvalue theory |
| title_short |
On some Banach space constants arising in nonlinear fixed point and eigenvalue theory |
| title_full |
On some Banach space constants arising in nonlinear fixed point and eigenvalue theory |
| title_fullStr |
On some Banach space constants arising in nonlinear fixed point and eigenvalue theory |
| title_full_unstemmed |
On some Banach space constants arising in nonlinear fixed point and eigenvalue theory |
| title_sort |
on some banach space constants arising in nonlinear fixed point and eigenvalue theory |
| publisher |
SpringerOpen |
| series |
Fixed Point Theory and Applications |
| issn |
1687-1820 1687-1812 |
| publishDate |
2004-12-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/S1687182004406068 |
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