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

Penot, Jean-Paul

doi:10.1090/S0002-9939-1985-0766542-6

A characterization of Clarke’s strict tangent cone via nonlinear semigroups
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Proc. Amer. Math. Soc. 93 (1985), 128-132 Request permission

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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Calcul différentiel

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