Extremality and differentiability of convex functions

• Autorzy: Bourass A. , Ferrahi B. , Saidou N.
• Języki publikacji: EN

Abstrakty

EN

We study relations between the differentiability and some geometrical properties of convex functions defined on a Banach space. As a consequence, we get a characterization of Radon-Nikodym property in Banach spaces by geometrical properties of convex functions.

Słowa kluczowe

EN

differentiability; convex functions; dentability; strongly exposed; Radon-Nikodym property; rotundity

PL

różniczkowalność; funkcja wypukła; silnie wyeksponowany; własność Radona-Nikodyma

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2003
• Tom: Vol. 51, no 1
• Strony: 13--29
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Bourass A.

• Département de Mathématiques et Informatiques, Faculté des Sciences de Rabat, Université Mohamed V-Agdal, B.P. 1014, Rabat, Morocco

autor

Ferrahi B.

• Département de Mathématiques et Informatiques, Faculté des Sciences de Rabat, Université Mohamed V-Agdal, B.P. 1014, Rabat, Morocco

autor

Saidou N.

• Département de Mathématiques et Informatiques, Faculté des Sciences de Rabat, Université Mohamed V-Agdal, B.P. 1014, Rabat, Morocco

Bibliografia

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• [2] J. Bourgain, On dentability and Bishop-Phelps property, Israel J. Math., 28 (1977) 265-271.
• [3] J. Bourgain, La propriété de Radon-Nikodým, Publ. Math. Uniw. Pierre et Marie Curie, 36 (1979).
• [4] J. Bourgain, Geometric aspects of convex sets with the Radon-Nikodým property, Lecture Notes in Math., 993, Springer-Velag, Berlin New York 1983.
• [5] C. Castaing, C. Valadier, Convex analysis and measurable multifunctions, Lecture Notes in Math., 580, Springer-Verlag, Berlin New York 1977.
• [6] J. B. Collier, The dual of a space with the Radon- Nikodým property, Pacific J. Math., 64 (1976) 103-106.
• [7] J. Diestel, J. J. Uhl, Vector measures, Math. Surveys Monogr., 15 (1977).
• [8] B. L. Lin, P. K. Lin, L. S. Troyanski, A characterization of denting points of a closed bounded convex set, Proc. Amer. Math. Soc., 345 (1988) 526-528.
• [9] R. R. Phelps, Convex functions, monotone operators and differentiability, Lecture Notes in Math., 1364 (1988).
• [10] W. Schachermayer, A. Sersouri, E. Werner, Moduli of nondentability and the Radon-Nikodým property in Banach spaces, Israel J. Math., 65 (3) (1989) 225-256.