# Minimal pairs of bounded closed convex sets

Studia Mathematica (1997)

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

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topGrzybowski, 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

top- [1] V. F. Dem'yanov and A. M. Rubinov, Quasidifferential Calculus, Optimization Software Inc., New York, 1986.
- [2] J. Grzybowski, Minimal pairs of compact convex sets, Arch. Math. (Basel) 63 (1994), 173-181. Zbl0804.52002
- [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] S. Scholtes, Minimal pairs of convex bodies in two dimensions, Mathematika 39 (1992), 267-273. Zbl0759.52004
- [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] M. Wiernowolski, On amount of minimal pairs, Funct. Approx. Comment. Math. 23 (1994), 35-39. Zbl0838.52005

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