# 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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