Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
Let 𝔼 be a strictly convex separable Banach space of dimension at least 2. Let K(𝔼) be the space of all nonempty compact convex subsets of 𝔼 endowed with the Hausdorff distance. Denote by $K^0$ the set of all X ∈ K(𝔼) such that the farthest distance mapping $a ↦ M_X(a)$ is multivalued on a dense subset of 𝔼. It is proved that $K^0$ is a residual dense subset of K(𝔼).
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
99-107
Opis fizyczny
Daty
wydano
1995
otrzymano
1991-10-18
poprawiono
1992-12-14
Twórcy
autor
- Centro Matematico V. Volterra, Università di Roma II, Via della Ricerca Scientifica, 00133 Roma, Italy
autor
- Dipartimento di Matematica, Università dell'Aquila, Via Vetoio, 67010 Coppito (L'Aquila), Italy
Bibliografia
- [1] E. Asplund, Farthest points in reflexive locally uniformly rotund Banach spaces, Israel J. Math. 4 (1966), 213-216.
- [2] K. Bartke and H. Berens, Eine Beschreibung der Nichteindeutigkeitsmenge für die beste Approximation in der Euklidischen Ebene, J. Approx. Theory 47 (1986), 54-74.
- [3] J. M. Borwein and S. Fitzpatrick, Existence of nearest points in Banach spaces, Canad. J. Math. 41 (1989), 702-720.
- [4] F. S. De Blasi, J. Myjak and P. L. Papini, Porous sets in best approximation theory, J. London Math. Soc. (2) 44 (1991), 135-142.
- [5] R. Deville and V. Zizler, Farthest points in w*-compact sets, Bull. Austral. Math. Soc. 38 (1988), 433-439.
- [6] N. Dunford and J. T. Schwartz, Linear Operators, Vol. I, Interscience, New York, 1958.
- [7] M. Edelstein, Farthest points of sets in uniformly convex Banach spaces, Israel J. Math. 4 (1966), 171-176.
- [8] P. M. Gruber, Die meisten konvexen Körper sind glatt, aber nicht zu glatt, Math. Ann. 229 (1977), 259-266.
- [9] K. S. Lau, Farthest points in weakly compact sets, Israel J. Math. 22 (1975), 168-174.
- [10] V. Klee, Some new results on smoothness and rotundity in normed linear spaces, Math. Ann. 139 (1959), 51-63.
- [11] S. Miyajima and F. Wada, Uniqueness of a farthest point in a bounded closed set in Banach spaces, preprint.
- [12] B. B. Panda and K. Dwivedi, On existence of farthest points, Indian J. Pure Appl. Math. 16 (1985), 486-490.
- [13] T. Zajíček, On the Fréchet differentiability of distance functions, Rend. Circ. Mat. Palermo (2) Suppl. 5 (1985), 161-165.
- [14] T. Zamfirescu, Using Baire category in geometry, Rend. Sem. Mat. Univers. Politec. Torino 43 (1985), 67-88.
- [15] T. Zamfirescu, The nearest point mapping is single valued nearly everywhere, Arch. Math. (Basel) 54 (1990), 563-566.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv112i2p99bwm