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Abstrakty
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.
Wydawca
Rocznik
Tom
Strony
13--29
Opis fizyczny
Bibliogr. 10 poz.
Twórcy
autor
- Département de Mathématiques et Informatiques, Faculté des Sciences de Rabat, Université Mohamed V-Agdal, B.P. 1014, Rabat, Morocco
autor
- Département de Mathématiques et Informatiques, Faculté des Sciences de Rabat, Université Mohamed V-Agdal, B.P. 1014, Rabat, Morocco
autor
- Département de Mathématiques et Informatiques, Faculté des Sciences de Rabat, Université Mohamed V-Agdal, B.P. 1014, Rabat, Morocco
Bibliografia
- [1] E. Asplund, R. T. Rockafellar, Gradients of convex functions, Trans. Amer. Math. Soc., 139 (1969) 433-467.
- [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.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0001-0043