On minimax theorems for sets closed in measure

Автор: Bukhvalov Alexander Vasilevich, Martellotti Anna

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 1 т.6, 2004 года.

Бесплатный доступ

This article is devoted to the Ky Fan minimax theorem for convex sets closed in measure in L^1. In general, these sets do not carry any formal compactness properties for any reasonable topology.

Короткий адрес: https://sciup.org/14318102

IDR: 14318102

Список литературы On minimax theorems for sets closed in measure

Berezhnoi E. I. On a theorem by G. Ya. Lozanovskii//Izv. Vyssh. Uchebn. Zaved. Matematika.-1982.-№ 2.-P. 81-83. [Russian]; English transl.: Soviet Math. (Iz. VUZ).
Berezhnoi E. I. On a theorem by G. Ya. Lozanovskii//In: Qualitative and approximate methods of the investigation of operator equations.-Jaroslavl', 1983.-P. 3-18. [Russian]
Besbes M. Points fixes des contractions definies sur un convexe L^0-ferme de L^1//C. R. Acad. Sci. Paris. Serie I.-1990.-V. 311.-P. 243-246.
Borovkov A. A. Mathematical Statistics: Special Topics.-Moscow: Nauka, 1984. [Russian]
Borwein J. M., Zhuang D. On Fan's minimax theorem//Math. Progr.-1986.-V. 34.-P. 232-234.
Bukhvalov A. V. Optimization without compactness, and its applications//In: Operator Theory in Function Spaces and Banach Lattices. Operator Theory. Advances and Applications.-Basel, Birkhauser, 1995.-V. 75.-P. 95-112.
Bukhvalov A V., Lozanovskii G. Ya. On sets closed with respect to convergence in measure in spaces of measurable functions//Dokl. Akad. Nauk SSSR.-1973.-V. 212.-P. 1273-1275. [Russian]; English transl.: Soviet Math. Dokl.-1973.-V. 14.-P. 1563-1565.
Delbaen F., Schachermayer W. A general version of the fundamental theorem of asset pricing//Math. Ann.-1994.-V. 300.-P. 463-520.
Granas A., Liu F. C. Some minimax theorems without convexity//In: Non Linear and Convex Analysis -Proceedings in Honor of Ky Fan (B. L. Lin and S. Simons Eds.).-Dekker, New York.-1987.-V. 107.-P. 61-75.-(Lecture Notes in Pure and Applied mathematics).
Janovskii L. P. Some theorems of nonlinear analysis in non-reflexive Banach spaces//In: Proc. XV-th School on the Theory of Operators in Function Spaces. Part II.-Ul'yanovsk, 1990.-P. 136. [Russian]
Kantorovich L. V., Akilov G. P. Functional Analysis.-Moscow: Nauka, 1977. [Russian]; English transl.: Oxford: Pergamon Press, 1982.
Lehmann E. L., Casella G. Theory of Point Estimation.-Springer, 1998.
Levin L. V. Extremal problems with convex functionals that are lower semicontinuous with respect to convergence in measure//Dokl. Akad. Nauk SSSR.-1975.-V. 224, № 6.-P. 1256-1259. [Russian]; English transl.: Soviet Math. Dokl.-1976.-V. 16, № 5.-P. 1384-1388.
Lozanovskii G. Ya. On some Banach lattices. IV//Sibirsk. Mat. Zh.-1973.-V. 14.-P. 140-155. [Russian]; English transl.: Siberian. Math. J.-1973.-V. 14.-P. 97-108.
Lozanovskii G. Ya. On transformations of Banach lattices of measurable functions//Izv. Vyssh. Uchebn. Zaved. Matematika.-1978.-№ 5.-P. 84-86. [Russian]; English transl.: Soviet Math. (Iz. VUZ).
Lozanovskii G. Ya. Transformations of ideal Banach spaces by means of concave functions//In: Qualitative and Approximate Methods of the Investigation of Operator Equations.-Jaroslavl', 1978.-V. 3.-P. 122-147. [Russian]
Martellotti A., Salvadori A. A minimax theorem for functions taking values in a Riesz space//J. Math. Anal. Appl.-1988.-V. 133.-P. 1-13.
Maurey B. Theoremes de factorisation pour les operateurs lineaires a valeurs dans les espaces L_p//Asterisque.-1974.-№ 11.
Reisner S. On two theorems of Lozanovskii concerning intermediate Banach lattices//Lect. Notes Math.-1988.-1317.-P. 67-83.
Werner D. A proof of the Markov-Kakutani fixed point theorem via the Hahn-Banach theorem//Extracta Math.-1993.-V. 8.-P. 37-38.

Еще

Статья научная