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“Solar” properties of sets in Banach spaces

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Abstract

In this article we consider relations between different classes of “suns.” A sufficient condition for a set to be a “sun” is given.

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Literature cited

  1. N. V. Efimov and S. B. Stechkin, “Some properties of Tchebyshev sets,” Dokl. Akad. Nauk SSSR,118, No. 1, 17–19 (1958).

    Google Scholar 

  2. N. V. Efimov and S. B. Stechkin, “Supporting properties of sets in Banach spaces and Tchebyshev sets,” Dokl. Akad. Nauk SSSR,127, No. 2, 254–257 (1959).

    Google Scholar 

  3. S. Eilenberg and D. Montgomery, “Fixed point theorems for multivalued transformations,” Amer. J. Math.,68, No. 2, 214–222 (1946).

    Google Scholar 

  4. V. L. Klee, “Remarks on nearest points in normed linear spaces,” Proc. Colloq. Convexity, Copenhagen, 1965, 168–176 (1967).

    Google Scholar 

  5. L. P. Vlasov, “Tchebyshev sets and some of their generalizations,” Matem. Zametki,3, No. 1, 59–69 (1968).

    Google Scholar 

  6. L. P. Vlasov, “Approximate properties of sets in Banach spaces,” Matem. Zametki,7, No. 5, 593–604 (1970).

    Google Scholar 

  7. L. P. Vlasov, “Some theorems about Tchebyshev sets,” Matem. Zametki,11, No. 2, 135–144 (1972).

    Google Scholar 

  8. L. P. Vlasov, “Approximately convex sets in Banach spaces,” Dokl. Akad. Nauk SSSR,163, No. 1, 18–21 (1965).

    Google Scholar 

  9. M. M. Day, Normed Linear Spaces, Springer Verlag, Berlin and New York (1958).

    Google Scholar 

  10. E. V. Oshman, “Continuity of a metric projection and some geometric properties of the unit sphere in a Banach space,” Dokl. Akad. Nauk SSSR,185, No. 1, 34–36 (1969).

    Google Scholar 

  11. B. Brosowski, “Fixpunktsätze in der Approximationstheorie,” Mathematica (Cluj),11, No. 2, 195–220 (1969).

    Google Scholar 

  12. B. Brosowski, “Über eine Fixpunkteigenschaft der metrischen Projection,” Computing,5, 295–302 (1970).

    Google Scholar 

  13. K. Kuratowski, Topologie, Vol. 2, Hafner (1961).

  14. N. Dunford and J. Schwartz, Linear Operators, Vol. 1, Interscience Publishers, New York and London (1958).

    Google Scholar 

  15. G. Köthe, Topologische Lineare Räume I, Springer Verlag, Berlin, Heidelberg, and New York (1960).

    Google Scholar 

  16. K. Fan, “Fixed point and minimax theorems in locally convex topological linear spaces,” Proc. Nat. Acad. Sci.,38, 121–126 (1952).

    Google Scholar 

  17. V. L. Klee, “Remarks on nearest points in normed linear spaces,” Notices Amer. Math. Soc.,12, No. 7, 812 (1965).

    Google Scholar 

  18. L. P. Vlasov, “On Tchebyshev sets,” Dokl. Akad. Nauk SSSR,173, No. 3, 491–494 (1967).

    Google Scholar 

  19. B. Brosowski, K. H. Hoffman, E. Schäfer, and H. Weber, “Stetigkeitssätze für metrische Projectionen, III, Eine Fixpunkteigenschaft der metrischen Projectionen,” MPI-PAE/Astro, München,12 (1969).

    Google Scholar 

  20. J. Blatter, P. D. Morris, and D. E. Wulbert, “Continuity of a set-valued metric projection,” Math. Ann.,178, No. 1, 12–24 (1968).

    Google Scholar 

  21. J. Blatter, “Zur Stetigkeit von mengenwertigen metrischen Projectionen,” Forschungsber, Landes Nordnhein-westfalen, No. 1870, 17–38 (1967).

    Google Scholar 

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Translated from Matematicheskie Zametki, Vol. 13, No. 6, pp. 795–805, June, 1973.

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Vlasov, L.P. “Solar” properties of sets in Banach spaces. Mathematical Notes of the Academy of Sciences of the USSR 13, 477–482 (1973). https://doi.org/10.1007/BF01163954

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  • DOI: https://doi.org/10.1007/BF01163954

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