10 resultados para Weak Hyperbolicity

em Bulgarian Digital Mathematics Library at IMI-BAS


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2002 Mathematics Subject Classification: 35S05, 47G30, 58J42.

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∗ Partially supported by INTAS grant 97-1644

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Research partially supported by INTAS grant 97-1644

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* Partially supported by Universita` di Bari: progetto “Strutture algebriche, geometriche e descrizione degli invarianti ad esse associate”.

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We are concerned with two-level optimization problems called strongweak Stackelberg problems, generalizing the class of Stackelberg problems in the strong and weak sense. In order to handle the fact that the considered two-level optimization problems may fail to have a solution under mild assumptions, we consider a regularization involving ε-approximate optimal solutions in the lower level problems. We prove the existence of optimal solutions for such regularized problems and present some approximation results when the parameter ǫ goes to zero. Finally, as an example, we consider an optimization problem associated to a best bound given in [2] for a system of nondifferentiable convex inequalities.

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The main concern of this paper is to present some improvements to results on the existence or non-existence of countably additive Borel measures that are not Radon measures on Banach spaces taken with their weak topologies, on the standard axioms (ZFC) of set-theory. However, to put the results in perspective we shall need to say something about consistency results concerning measurable cardinals.

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2000 Mathematics Subject Classification: 47H10, 54E15.

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2000 Mathematics Subject Classification: 60J27, 60K25.

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2000 Mathematics Subject Classification: 60G18, 60E07

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2000 Mathematics Subject Classification: 54H25, 47H10.