Summary
A set-valued functionF from a coneC with a cone-basis of a topological vector spaceX into the family of all non-empty compact convex subsets of a locally convex spaceY is called superadditive provided thatF(x) + F(y) ⊂ F(x + y), for allx, y ∈ C. We show that every superadditive set-valued function admits an additive selection.
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Dedicated to Professor Otto Haupt on his 100th birthday
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Smajdor, A. Additive selections of superadditive set-valued functions. Aeq. Math. 39, 121–128 (1990). https://doi.org/10.1007/BF01833142
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DOI: https://doi.org/10.1007/BF01833142