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On Jensen’s functional equation for set-valued functions. (English) Zbl 0628.39013
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.
Reviewer: N.Ghircoiaşiu

##### MSC:
 39B52 Functional equations for functions with more general domains and/or ranges 54C60 Set-valued maps in general topology