Some properties of convex and *-concave multifunctions
Abstract
We investigate some properties of *-concave and convex multifunctions on the real line with convex bounded closed values. In particularly we consider the Hadamard inequality and the Hardy–Littlewood–Pólya majorization theory in the case of multifunctions.
References
C. Castaing, M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics 580, Springer-Verlag, Berlin–Heidelberg–New York, 1977.
##plugins.generic.googleScholarLinks.settings.viewInGS##
F.S. de Blasi, On the differentiability of multifunctions, Pacific J. Math. 66 (1976), 67-81.
##plugins.generic.googleScholarLinks.settings.viewInGS##
A. Dinghas, Zum Minkowskischen Integralbegriff abgeschlossener Mengen, Math. Z. 66 (1956), 173–188.
##plugins.generic.googleScholarLinks.settings.viewInGS##
M. Hukuhara, Intégration des applications mesurables dont la valeur est un compact convexe, Funkcial. Ekvac. 10 (1967), 205–223.
##plugins.generic.googleScholarLinks.settings.viewInGS##
M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities. Cauchy’s Equation and Jensen’s Inequality, PWN (Polish Scientific Publishers) and Uniwersytet Śląski, Warszawa–Kraków–Katowice, 1985.
##plugins.generic.googleScholarLinks.settings.viewInGS##
J. Matkowski, K. Nikodem, An integral Jensen inequality for convex multifunctions, Result. Math. 26 (1994), 348-353.
##plugins.generic.googleScholarLinks.settings.viewInGS##
K. Nikodem, K-convex and K-concave set-valued functions, Zeszyty Naukowe Politechniki Łódzkiej, Mat. 559, Rozprawy Naukowe 114, Łódź, 1989.
##plugins.generic.googleScholarLinks.settings.viewInGS##
B. Piątek, On the Sincov functional equation, Demonstratio Math. 38 (2005), 875–881.
##plugins.generic.googleScholarLinks.settings.viewInGS##
E. Sadowska, Hadamard inequality and a refinement of Jensen inequality for set-valued functions, Result. Math. 32 (1997), 332-337.
##plugins.generic.googleScholarLinks.settings.viewInGS##
W. Smajdor, Note on a Jensen type functional equation, Publicationes Math. Debrecen 63(4) (2003), 703-714.
##plugins.generic.googleScholarLinks.settings.viewInGS##
R. Urbański, A generalization of Minkowski–Rådström–Hörmander theorem, Bull. Akad. Pol. Sci. 24 (1976), no. 9, 709–715.
##plugins.generic.googleScholarLinks.settings.viewInGS##
