منابع مشابه
Epi-Lipschitzian reachable sets of differential inclusions
The reachable sets of a differential inclusion have nonsmooth topological boundaries in general. The main result of this paper is that under the well–known assumptions of Filippov’s existence theorem (about solutions of differential inclusions), every epi-Lipschitzian initial compact set K ⊂ RN preserves this regularity for a short time, i.e. θF (t, K) is also epi-Lipschitzian for all small t >...
متن کاملCompactly Epi-lipschitzian Convex Sets and Functions in Normed Spaces
The concept of compactly epi-Lipschitzian (CEL) sets in locally convex topological spaces was introduced by Borwein and Strojwas [6]. It is an extension of Rockafellar’s concept of epi-Lipschitzian sets [36]. An advantage of the CEL property is that it always holds in finite dimensional spaces and, in contrast to its epi-Lipschitzian predecessor, makes it possible to recapture much of the detai...
متن کاملSMOOTH NORMAL APPROXIMATIONS OF EPI-LIPSCHITZIAN SUBSETS OF Rn∗
A sequence (Mk) of closed subsets of Rn converges normally to M ⊂ Rn if (sc) M = lim supMk = lim inf Mk in the sense of Painlevé–Kuratowski and (nc) lim sup G(NMk ) ⊂ G(NM ), where G(NM ) (resp., G(NMk )) denotes the graph of NM (resp., NMk ), Clarke’s normal cone to M (resp., Mk). This paper studies the normal convergence of subsets of Rn and mainly shows two results. The first result states t...
متن کاملcompactifications and representations of transformation semigroups
this thesis deals essentially (but not from all aspects) with the extension of the notion of semigroup compactification and the construction of a general theory of semitopological nonaffine (affine) transformation semigroup compactifications. it determines those compactification which are universal with respect to some algebric or topological properties. as an application of the theory, it is i...
15 صفحه اولTube Representations of Ordered Sets
We define the (n, i, f)-tube orders, which include interval orders, trapezoid orders, triangle orders, weak orders, order dimension n, and interval-orderdimension n as special cases. We investigate some basic properties of (n, i, f)-tube orders, and begin classifying them by containment.
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ژورنال
عنوان ژورنال: Nonlinear Analysis: Theory, Methods & Applications
سال: 2010
ISSN: 0362-546X
DOI: 10.1016/j.na.2010.05.027