Nonexpansive retractions in Hilbert spaces
Annales UMCS, Mathematica (2009)
- Volume: 63, Issue: 1, page 83-90
- ISSN: 2083-7402
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topKazimierz Goebel, and Ewa Sędłak. "Nonexpansive retractions in Hilbert spaces." Annales UMCS, Mathematica 63.1 (2009): 83-90. <http://eudml.org/doc/267672>.
@article{KazimierzGoebel2009,
abstract = {Let H be a Hilbert space and C ⊂ H be closed and convex. The mapping P: H → C known as the nearest point projection is nonexpansive (1-lipschitzian). We observed that, the natural question: "Are there nonexpansive projections Q: H → C other than P?" is neglected in the literature. Also, the answer is not often present in the "folklore" of the Hilbert space theory. We provide here the answer and discuss some facts connected with the subject.},
author = {Kazimierz Goebel, Ewa Sędłak},
journal = {Annales UMCS, Mathematica},
keywords = {Hilbert space; convex sets; retractions; nonexpansive mappings; nonexpansive map; retraction},
language = {eng},
number = {1},
pages = {83-90},
title = {Nonexpansive retractions in Hilbert spaces},
url = {http://eudml.org/doc/267672},
volume = {63},
year = {2009},
}
TY - JOUR
AU - Kazimierz Goebel
AU - Ewa Sędłak
TI - Nonexpansive retractions in Hilbert spaces
JO - Annales UMCS, Mathematica
PY - 2009
VL - 63
IS - 1
SP - 83
EP - 90
AB - Let H be a Hilbert space and C ⊂ H be closed and convex. The mapping P: H → C known as the nearest point projection is nonexpansive (1-lipschitzian). We observed that, the natural question: "Are there nonexpansive projections Q: H → C other than P?" is neglected in the literature. Also, the answer is not often present in the "folklore" of the Hilbert space theory. We provide here the answer and discuss some facts connected with the subject.
LA - eng
KW - Hilbert space; convex sets; retractions; nonexpansive mappings; nonexpansive map; retraction
UR - http://eudml.org/doc/267672
ER -
References
top- Goebel, K., Kirk, W. A., Topics in Metric Fixed Point Theory, Cambridge Univ. Press, Cambridge, 1990. Zbl0708.47031
- Kirzbraun, M. D., Über die Zussamenziehende und Lipschistsche Transformationen, Fund. Math. 22 (1934), 77-108.
- Valentine, F. A., A Lipschitz condition preserving extension for a vectpr function, Amer. J. Math. 67 (1945), 83-93. Zbl0061.37507
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