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Fundam. Prikl. Mat., 2016, Volume 21, Issue 4, Pages 23–66 (Mi fpm1747)  

A separation theorem for nonconvex sets and its applications

G. E. Ivanova, M. S. Lopushanskiab

a Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We prove theorems on separation by sphere or (in a general case) by the boundary of a shifted quasiball of two closed disjoint subsets of a Banach space one of which is prox-regular or weakly convex and the other is a summand of a ball or quasiball. These separation theorems are applied for proving some theorems on the continuity of the intersection of two multifunctions, the values of one of them being prox-regular or weakly convex (nonconvex, in general), and the values of the other being convex and summands of a ball or quasiball. As a corollary, a theorem on the continuity of a multifunction with values bounded by the graphs of two functions is obtained.

Funding Agency Grant Number
Russian Science Foundation 14-11-00443


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Bibliographic databases:

UDC: 517.982.252

Citation: G. E. Ivanov, M. S. Lopushanski, “A separation theorem for nonconvex sets and its applications”, Fundam. Prikl. Mat., 21:4 (2016), 23–66

Citation in format AMSBIB
\Bibitem{IvaLop16}
\by G.~E.~Ivanov, M.~S.~Lopushanski
\paper A separation theorem for nonconvex sets and its applications
\jour Fundam. Prikl. Mat.
\yr 2016
\vol 21
\issue 4
\pages 23--66
\mathnet{http://mi.mathnet.ru/fpm1747}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3783796}


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  • Фундаментальная и прикладная математика
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