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
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.
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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
\by G.~E.~Ivanov, M.~S.~Lopushanski
\paper A separation theorem for nonconvex sets and its applications
\jour Fundam. Prikl. Mat.
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