Minimal pairs of bounded closed convex sets

J. Grzybowski; R. Urbański

Studia Mathematica (1997)

  • Volume: 126, Issue: 1, page 95-99
  • ISSN: 0039-3223

Abstract

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The existence of a minimal element in every equivalence class of pairs of bounded closed convex sets in a reflexive locally convex topological vector space is proved. An example of a non-reflexive Banach space with an equivalence class containing no minimal element is presented.

How to cite

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Grzybowski, J., and Urbański, R.. "Minimal pairs of bounded closed convex sets." Studia Mathematica 126.1 (1997): 95-99. <http://eudml.org/doc/216445>.

@article{Grzybowski1997,
abstract = {The existence of a minimal element in every equivalence class of pairs of bounded closed convex sets in a reflexive locally convex topological vector space is proved. An example of a non-reflexive Banach space with an equivalence class containing no minimal element is presented.},
author = {Grzybowski, J., Urbański, R.},
journal = {Studia Mathematica},
keywords = {convex analysis; pairs of convex sets; space of convex sets; minimal pair of sets},
language = {eng},
number = {1},
pages = {95-99},
title = {Minimal pairs of bounded closed convex sets},
url = {http://eudml.org/doc/216445},
volume = {126},
year = {1997},
}

TY - JOUR
AU - Grzybowski, J.
AU - Urbański, R.
TI - Minimal pairs of bounded closed convex sets
JO - Studia Mathematica
PY - 1997
VL - 126
IS - 1
SP - 95
EP - 99
AB - The existence of a minimal element in every equivalence class of pairs of bounded closed convex sets in a reflexive locally convex topological vector space is proved. An example of a non-reflexive Banach space with an equivalence class containing no minimal element is presented.
LA - eng
KW - convex analysis; pairs of convex sets; space of convex sets; minimal pair of sets
UR - http://eudml.org/doc/216445
ER -

References

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  1. [1] V. F. Dem'yanov and A. M. Rubinov, Quasidifferential Calculus, Optimization Software Inc., New York, 1986. 
  2. [2] J. Grzybowski, Minimal pairs of compact convex sets, Arch. Math. (Basel) 63 (1994), 173-181. Zbl0804.52002
  3. [3] D. Pallaschke, S. Scholtes and R. Urbański, On minimal pairs of compact convex sets, Bull. Polish Acad. Sci. Math. 39 (1991), 1-5. Zbl0759.52003
  4. [4] S. Scholtes, Minimal pairs of convex bodies in two dimensions, Mathematika 39 (1992), 267-273. Zbl0759.52004
  5. [5] R. Urbański, A generalization of the Minkowski-Rå dström-Hörmander theorem, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), 709-715. Zbl0336.46009
  6. [6] M. Wiernowolski, On amount of minimal pairs, Funct. Approx. Comment. Math. 23 (1994), 35-39. Zbl0838.52005

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