an:04021794
Zbl 0628.39013
Nikodem, Kazimierz
On Jensen's functional equation for set-valued functions
EN
Rad. Mat. 3, 23-33 (1987).
00153444
1987
j
39B52 54C60
Cauchy's functional equation; locally convex topological vector space; Jensen's functional equation; set-valued solutions
The set-valued function F: [0,\(\infty)\to C(X)\) (where C(X) denotes the family of all compact subsets of a locally convex topological vector space X) satisfies Jensen's functional equation iff it has the form \(F(s)=f(s)+sH+K\), \(s\in [0,\infty)\), where f is an additive function and H, K are compact and convex subsets of X. Some other theorems characterizing set-valued solutions of Cauchy's and Jensen's equations are also given.
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