On concave iteration semigroups of linear set-valued functions

• Autores: Andrzej Smajdor
• Localización: Aequationes mathematicae, ISSN 0001-9054, Vol. 75, Nº. 1-2, 2008, págs. 149-162
• Idioma: inglés
• DOI: 10.1007/s00010-007-2876-8
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• Resumen

  • Let K be a closed convex cone in a real Banach space and let cc(K) denote the family of all nonempty convex compact subsets of K. Let I(x) = {x} for x ? K. Suppose that G : K ? cc(K) is a given continuous linear multivalued map such that 0 ? G(x) for x ? K. It is proved that a family {F t : t = 0} of linear continuous set-valued functions F t , where is an iteration semigroup if and only if the equality holds true. It is also proved that a concave iteration semigroup of continuous linear set-valued functions with the infinitesimal generator G fulfilling (b) and such that 0 ? G(x) is of the form (a).