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2011, vol. 15, br. 1, str. 1-6
Perturbation of farthest points in weakly compact sets
(naslov ne postoji na srpskom)
Department of Mathematics, University Bordeaux, Talence, France

e-adresajean-matthieu.auge@math.u-bordeaux1.fr
Ključne reči: normed space; weakly compact set; farthest points
Sažetak
(ne postoji na srpskom)
If ƒ is a real valued weakly lower semi-continuous function on a Banach space X and C a weakly compact subset of X, we show that the set of x Є X such that z → ‌‌‌||‌‌‌‌x-z ||- ƒ(z) attains its supremum on C is dense in X. We also construct a counter example showing that the set of x Є X such that z → ‌‌‌||‌‌‌‌x-z ||+ ||z || - attains its supremum on C is not always dense in X.
Reference
Asplund, E. (1966) Farthest points in reflexive locally uniformly rotund Banach spaces. Israel Journal of Mathematics, 4(4): 213-216
Edelstein, M. (1966) Farthest points of sets in uniformly convex banach spaces. Israel Journal of Mathematics, 4(3): 171-176
Hejazian, S., Niknam, A., Shadkam, S. (2008) Farthest Points and Subdifferential in p-Normed Spaces. Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences, Volume 2008 Article ID 196326, 6 pages
Lau, K. (1975) Farthest points in weakly compact sets. Israel Journal of Mathematics, 22(2): 168-174
Wang, X. On Chebyshev functions and Klee functions. Journal of Mathematical Analysis and Applications
 

O članku

jezik rada: engleski
vrsta rada: neklasifikovan
DOI: 10.5937/MatMor1101001A
objavljen u SCIndeksu: 27.03.2012.

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