Skip to content

Go to Sitemap

Download PDF - Polynomial set-valued functions All rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Polynomial set-valued functions

Authors ¹

Affiliations

Institute of Mathematics, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland

Abstract

The aim of this paper is to give a necessary and sufficient condition for a set-valued function to be a polynomial s.v. function of order at most 2.

Keywords

polynomial set-valued functions, difference operators, biadditive functions, Jensen function

C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Springer, Berlin, 1977.
R. Ger, On extensions of polynomial functions, Results Math. 26 (1994), 281-289.
M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, PWN and Uniw. Śl., Warszawa-Kraków-Katowice, 1985.
K. Nikodem, K-convex and K-concave set valued functions, Zeszyty Naukowe Politech. Łódzkiej, Mat. 559, Rozprawy Naukowe 114, 1989.
H. Rådström, An embedding theorem for spaces of convex sets, Proc. Amer. Math. Soc. 3 (1952), 165-169.
H. Rådström, One-parameter semigroups of subsets of a real linear space, Ark. Mat. 4 (1960), 87-97.
A. Smajdor, On a functional equation, Ann. Math. Sil. 8 (1994), 217-226.