Fixed point free maps of a closed ball with small measures of noncompactness.

Martin Väth

Collectanea Mathematica (2001)

  • Volume: 52, Issue: 2, page 101-116
  • ISSN: 0010-0757

Abstract

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We show that in all infinite-dimensional normed spaces it is possible to construct a fixed point free continuous map of the unit ball whose measure of noncompactness is bounded by 2. Moreover, for a large class of spaces (containing separable spaces, Hilbert spaces and l-infinity (S)) even the best possible bound 1 is attained for certain measures of noncompactness.

How to cite

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Väth, Martin. "Fixed point free maps of a closed ball with small measures of noncompactness.." Collectanea Mathematica 52.2 (2001): 101-116. <http://eudml.org/doc/42727>.

@article{Väth2001,
abstract = {We show that in all infinite-dimensional normed spaces it is possible to construct a fixed point free continuous map of the unit ball whose measure of noncompactness is bounded by 2. Moreover, for a large class of spaces (containing separable spaces, Hilbert spaces and l-infinity (S)) even the best possible bound 1 is attained for certain measures of noncompactness.},
author = {Väth, Martin},
journal = {Collectanea Mathematica},
keywords = {Compacidad; Punto fijo; Espacios normados; measure of noncompactness; fixed point; condensing operator},
language = {eng},
number = {2},
pages = {101-116},
title = {Fixed point free maps of a closed ball with small measures of noncompactness.},
url = {http://eudml.org/doc/42727},
volume = {52},
year = {2001},
}

TY - JOUR
AU - Väth, Martin
TI - Fixed point free maps of a closed ball with small measures of noncompactness.
JO - Collectanea Mathematica
PY - 2001
VL - 52
IS - 2
SP - 101
EP - 116
AB - We show that in all infinite-dimensional normed spaces it is possible to construct a fixed point free continuous map of the unit ball whose measure of noncompactness is bounded by 2. Moreover, for a large class of spaces (containing separable spaces, Hilbert spaces and l-infinity (S)) even the best possible bound 1 is attained for certain measures of noncompactness.
LA - eng
KW - Compacidad; Punto fijo; Espacios normados; measure of noncompactness; fixed point; condensing operator
UR - http://eudml.org/doc/42727
ER -

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