# The Demyanov metric and some other metrics in the family of convex sets

Open Mathematics (2012)

- Volume: 10, Issue: 6, page 2229-2239
- ISSN: 2391-5455

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topTadeusz Rzeżuchowski. "The Demyanov metric and some other metrics in the family of convex sets." Open Mathematics 10.6 (2012): 2229-2239. <http://eudml.org/doc/269366>.

@article{TadeuszRzeżuchowski2012,

abstract = {We describe some known metrics in the family of convex sets which are stronger than the Hausdorff metric and propose a new one. These stronger metrics preserve in some sense the facial structure of convex sets under small changes of sets.},

author = {Tadeusz Rzeżuchowski},

journal = {Open Mathematics},

keywords = {Demyanov metric; Hausdorff metric; Convex sets; Small changes of sets; convex sets; small changes of sets},

language = {eng},

number = {6},

pages = {2229-2239},

title = {The Demyanov metric and some other metrics in the family of convex sets},

url = {http://eudml.org/doc/269366},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Tadeusz Rzeżuchowski

TI - The Demyanov metric and some other metrics in the family of convex sets

JO - Open Mathematics

PY - 2012

VL - 10

IS - 6

SP - 2229

EP - 2239

AB - We describe some known metrics in the family of convex sets which are stronger than the Hausdorff metric and propose a new one. These stronger metrics preserve in some sense the facial structure of convex sets under small changes of sets.

LA - eng

KW - Demyanov metric; Hausdorff metric; Convex sets; Small changes of sets; convex sets; small changes of sets

UR - http://eudml.org/doc/269366

ER -

## References

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- [7] Lesniewski A., Rzezuchowski T., The Demyanov metric for convex, bounded sets and existence of Lipschitzian Selectors, J. Convex Anal., 2011, 18(3), 737–747 Zbl1227.52002
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