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A characterization of Clarke's strict tangent cone via nonlinear semigroups


Author: Jean-Paul Penot
Journal: Proc. Amer. Math. Soc. 93 (1985), 128-132
MSC: Primary 90C48; Secondary 49A52
DOI: https://doi.org/10.1090/S0002-9939-1985-0766542-6
MathSciNet review: 766542
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Abstract: Clarke's strict tangent cone $ T_X^ \uparrow (a)$ at $ a \in X$ to a closed subset of a Banach space $ E$ is shown to contain the limit inferior of tangent cones $ {T_X}(x)$ to $ X$ at $ x$ as $ x \to a$, $ x \in X$. Several characterizations of $ T_X^ \uparrow (a)$ are presented. As a consequence various tangential and subtangential conditions for continuous vector fields on $ X$ are shown to be equivalent.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0766542-6
Keywords: Distance function, flow invariance, limit inferior, semigroups, tangent cones, vector fields
Article copyright: © Copyright 1985 American Mathematical Society

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