Hull-concave set-valued functions
Abstract
A set-valued function F is called hull-concave if
F(tx + (1-t)y) ⊂ co(tF(x) + (1-t)F(y))
for all x,y from the domain of F and all t∈[0,1]. It is shown that if a hull-concave set-valued function F is defined on an open convex subset D of ℝn and for every x∈D the set clF(x) is convex and bounded, then F is continuous on D. Some other properties of hull-concave set-valued functions are also given.
References
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Dipartimento di Matematica dell'Universita, Perugia, Italy Italy
Katedra Matematyki, Filia Politechniki Łódzkiej w Bielsku-Białej Poland
Dipartimento di Matematica dell'Universita, Perugia, Italy Italy
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