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Abstrakty
The existence of continuous selections is proved for a class of lower semicontinuous multifunctions whose values are closed convex subsets of a complete metric space equipped with an appropriate notion of convexity. The approach is based on the notion of pseudo-barycenter of an ordered n-tuple of points.
Wydawca
Rocznik
Tom
Strony
303--317
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
- Centro Vito Volterra, Dipartimento di Matematica, Università di Roma II (Tor Vergata), Via della Ricerca Scientifica, 00133 Roma, Italy
autor
- Dipartimento di Matematica per le Decisioni, Università di Firenze, Via Lombroso, 6/17, 50134 Firenze, Italy
Bibliografia
- [1] D. W. Curtis, Application of a selection theorem to hyperspace contractibility, Canad. J. Math. 27 (1985), 747-759.
- [2] F. S. De Blasi and G. Pianigiani, Approximate selections in α-convex metric spacer and topological degree, preprint n. 525, Centro Vito Volterra, Università di Roma „Tor Vergata", 2002.
- [3] J. Dugundji, Locally equiconnected spaces and absolute neighborhood retracts, Fund. Math. 57 (1965), 187-193.
- [4] -, Topology, Allyn and Bacon, Boston, 1966.
- [5] J. Dugundji and A. Granas, Fixed Point Theory, Vol. I, PWN-Polish Scientific Publ., Warszawa, 1982.
- [6] V. G. Gutev, Selection theorems under an assumption weaker than lower semicontinuity, Topology Appl. 50 (1993), 129-138.
- [7] S. Hu and N. S. Papageorgiou, Handbook of Multivalued Analysis, Vol. I, II, Kluwer, Dordrecht, 1997.
- [8] E. Michael, Continuous selections I , Ann. of Math. 63 (1956), 361-382.
- [9] -, Convex structure and continuous selections, Canad. J. Math. 11 (1959), 556-575.
- [10] -, Paraconvex sets, Math. Scand. 7 (1959), 372-376.
- [11] A. Nijenhuis, A note on hyperconvexity in Riemannian manifolds, Canad. J. Math. 11 (1959), 576-582.
- [12] L. Pasicki, Retracts in metric spaces, Proc. Amer. Math. Soc. 78 (1980), 595-600.
- [13] -, Applications of weeds, Zeszyty Nauk. Akad. Górn.-Hutniczej Mat.-Fiz.-Chem. 5 (1989), 89-108.
- [14] K. Przesławski and L. E. Rybiński, Michael selection theorem under weak Lower semicontinuity assumption, Proc. Amer. Math. Soc. 109 (1990), 537-543.
- [15] D. Repovš and P. V. Semenov, Continuous Selections of Multivalued Mappings, Kluwer, Dordrecht, 1998.
- [16] M. van de Vel, A selection theorem for topological convex structures, Trans. Amer. Math. Soc. 336 (1993), 463-496.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-BAT5-0004-0032