Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
In this paper we study Minkowski duality, i.e. the correspondence between sublinear functions and closed convex sets in the context of dual pairs of vector spaces.
Wydawca
Czasopismo
Rocznik
Tom
Strony
45--53
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
autor
- Faculty of Mathematics and Computer Science, Adam Mickiewicz University in Poznań, Umultowska 87, 61-614 Poznań, Poland
autor
- Institute of Operations, University of Karlsruhe (KIT), Kaiserstr. 12, D-76128 Karlsruhe, Germany
autor
- Faculty of Mathematics and Computer Science, Adam Mickiewicz University in Poznań, Umultowska 87, 61-614 Poznań, Poland
Bibliografia
- [1]. E. Caprari and J. P. Penot, Tangentially ds functions, Optimization 56 (2007), no. 1-2, 25-38, DOI 10.1080/02331930600816023.
- [2]. U. Cegrell, On the space of delta-convex functions and its dual, Bull. Math de la Soc. Sei. Math, de la R. S. de Roumaine 22 (1978), no. 70,133-139.
- [3]. V. F. Demyanov and A. M. Rubinov, Quasidifferential Calculus, Optimization Software Inc., Publications Division, New York 1986.
- [4]. V. Demyanov and A. Rubinov (eds.), Quasidifferentiability and related topics, Nonconvex Opti¬mization and its Applications, vol. 43, Kluwer Academic Publishers, Dordrecht 2000, xx+391, DOI 10.1007/978-1-4757-3137-8.
- [5]. L. Drewnowski, Additive and countably additive correspondences, Comment. Math. 19 (1976), 25-54.
- [6]. J. Grzybowski, M. Küçük, Y. Küçük, and R. Urbański, Minkowski-Rädström-Hörmander cone, Pac. J. Optim. 10 (2014), 649-666.
- [7]. J. Grzybowski and R. Urbański, Minimal pairs of bounded closed convex sets, Studia Math. 126 (1997), 95-99.
- [8]. L. Hörmander, Sur lafonction d’ appui des ensembles convexes dans un espace localement convexe, Arkiv for Matematik 3 (1954), 181-186.
- [9]. L. V. Kantorovich and G. P. Akilov, Funkctional Analysis, Pergamon Press, Oxford 1984.
- [10]. G. Köthe, Topological Vector Spaces, Vol. I, Springer Verlag, Berlin-Heidelberg-New York 1983.
- [11]. S. S. Kutateladze and A. M. Rubinov, Minkowski duality and its applications, Russ. Math. Surv. 27 (1972), no. 3,137-191.
- [12]. Le Van Hot, On the embedding theorem, Comment. Math. Universitatis Carolinae 4 (1980), 777-794.
- [13]. H. Minkowski, Allgemaine Lehrsätze über die konvexen Polyeder, Nachr. Ges. Wiss. Göttingen (1897), 198-210; reprinted in Gesammelte Abhandlungen, Vol. II, Teubner, Leipzig 1911,103-121.
- [14]. D. Pallaschke and R. Urbański, Pairs of Compact Convex Sets: Fractional Arithmetic with Convex Sets, Mathematics and its Applications, vol. 548, Kluwer Academic Publisher, Dordrecht-Boston-London 2002, DOI 10.1007/978-94-015-9920-7.
- [15]. G. Pinsker, The space of convex sets of a locally convex space, Trudy Leningrad Engineering-Economic Institute 63 (1966), 13-17.
- [16]. M. G. Rabinovich, An embedding theorem for space of convex sets (1967); English transl., Siberian Mathematical Journal 8, 275-279.
- [17]. H. Rädström, An embedding theorem for spaces of convex sets, Proc. Amer. Math. Soc. 3 (1952), 165-169. ¡
- [18]. K. D. Schmidt, Embedding theorems for classes of convex sets, Acta Appl. Math. 5 (1986), 209-237.
- [19]. R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Second expanded edition, Encyclopedia of Mathematics and its Applications, vol. 151, Cambridge University Press 2014.
- [20]. R. Urbanski, A generalization of the Minkowski-Rddstrom-Hdrmander theorem, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astr. Phys. 24 (1976), 709-715.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-e948718a-236a-4cd7-99fb-53b5eda470b7