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ISSN 1088-6826(online) ISSN 0002-9939(print)



A connectedness property of maximal monotone operators and its application to approximation theory

Author: Libor Veselý
Journal: Proc. Amer. Math. Soc. 115 (1992), 663-667
MSC: Primary 47H05; Secondary 41A65
MathSciNet review: 1095227
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Abstract: We prove a connectedness property of a general maximal monotone operator on a Hilbert space. As a consequence we easily obtain the characterization of components of the set of discontinuity points for metric projections of closed sets in Hilbert spaces. We show that these components are pathwise connected, too.

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  • [1] V. S. Balaganskii, On the connection between approximative and geometrical properties of sets, Approximation in Concrete and Abstract Banach Spaces, Akad. Nauk SSSR, Ural'skii Naučnyi Centr, pp. 46-53, 1987. (Russian) MR 945738 (89g:46023)
  • [2] H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland Math. Studies, no. 5, Amsterdam, 1973.
  • [3] R. Engelking, General topology, Monografie Matematyczne 60, Warszawa, 1977. MR 0500780 (58:18316b)
  • [4] J. R. Giles, Convex analysis with application in the differentiation of convex functions, Research Notes in Math., no. 58, Pitman, Boston 1982. MR 650456 (83g:46001)
  • [5] D. Pascali and S. Sburlan, Nonlinear mappings of monotone type, Bucuresti and Alphen aan den Rijn, 1978. MR 531036 (80g:47056)
  • [6] U. Westphal and J. Frerking, On a property of metric projections onto closed subsets of Hilbert spaces, Proc. Amer. Math. Soc. 105 (1989), 644-651. MR 946636 (89j:41051)

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Article copyright: © Copyright 1992 American Mathematical Society

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