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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Locally efficient monotone operators


Authors: Andrei Verona and Maria Elena Verona
Journal: Proc. Amer. Math. Soc. 109 (1990), 195-204
MSC: Primary 47H05; Secondary 49J52, 58C07
DOI: https://doi.org/10.1090/S0002-9939-1990-1012939-0
MathSciNet review: 1012939
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Abstract: We study monotone operators on quasi open or convex subsets of a real Banach space $ X$ (quasi open means that the contingent cone at each point equals $ X$). Among others we characterize the maximality of such an operator in terms of its $ {w^*}$-upper semicontinuity properties and, in the case of a convex domain, also in terms of its behavior at the support points. We next give sufficient conditions for such an operator to be generically single valued, extending Kenderov's theorems. As an application we reobtain generic Gâteaux and Fréchet differentiability results for convex functions defined on not necessarily open convex sets.


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DOI: https://doi.org/10.1090/S0002-9939-1990-1012939-0
Article copyright: © Copyright 1990 American Mathematical Society