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Stability estimates of continuous selections for metric almost-projections

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Literature cited

  1. F. Deutsch, “A survey of metric selections,”Contemporary Math.,18, 49–71 (1983).

    Google Scholar 

  2. F. Deutsch, W. Li, and S. H. Park, “Characterization of continuous and Lipschitz continuous metric selections in normed linear spaces,”J. Appr. Theory,58, No. 3, 297–314 (1989).

    Article  Google Scholar 

  3. A. L. Brown, “Set valued mappings, continuous selections, and metric projections,”J. Appr. Theory,57, No. 1, 48–68 (1989).

    Article  Google Scholar 

  4. S. V. Koniagin, “On continuous operators of generalized rational approximation,”Mat. Zametki,44, No. 3, 404 (1988).

    Google Scholar 

  5. I. G. Tsarkov, “Properties of sets having a continuous selection of the operatorP δ,”Mat. Zametki,48, No. 4, 122–131 (1990).

    Google Scholar 

  6. A. V. Marinov, “Stability ofε-quasi-solutions of operator equations of the first kind,” In:Approximation of functions by polynomials and spines [In Russian], Ural. Nauchn. Tsentr Akad. Nauk SSSR, Sverdlovsk (1985), pp. 105–117.

    Google Scholar 

  7. E. Michael, “Continuous selections,”J. Ann. Math., Ser 2,63, No. 2, 361–381 (1956).

    Google Scholar 

  8. M. I. Kadets, “On topological equivalency of uniformly convex spaces,”Uspekhi Mat. Nauk,10, No. 4, 137–141 (1955).

    Google Scholar 

  9. G. Distel,Geometry of Banach Spaces [In Russian], Vischa Shkola, Kiev (1980).

    Google Scholar 

  10. V. I. Berdyshev, “On the uniform continuity of the operator of best approximation,” In:Approximation Theory: Proc. Intern. Conf., Poznan (1972); PWN, Warsaw (1985), pp. 21–32.

    Google Scholar 

  11. V. I. Berdyshev, “Continuity of a set valued mapping related to the minimization problem for functionals,”Izv. Akad. Nauk SSSR, Ser. Mat.,44, No. 3, 483–509 (1980).

    Google Scholar 

  12. V. I. Berdyschev, “Norm variation in the problem of best approximation,”Mat. Zametki,29, No. 2, 181–196 (1981).

    Google Scholar 

  13. J. W. Daniel, “The continuity of metric projections as functions of the data,”J. Approx. Theory,12, No. 3, 234–240 (1974).

    Article  Google Scholar 

  14. K. Przeslwski, “Linear and Lipschitz continuous selections for the family of convex sets in Euclidean vector spaces,”Bull. Acad. Polon. Sci. Ser. Sci. Tech.,33, No. 1–2, 31–34 (1985).

    Google Scholar 

  15. G. C. Shepard, “The Steiner point of a convex polytope,”Can. J. Math.,18, No. 6, 1294–1300 (1966).

    Google Scholar 

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Authors and Affiliations

  1. The Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, USSR

    A. V. Marinov

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  1. A. V. Marinov
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Translated from Matematicheskie Zametki, Vol. 55, No. 4, pp. 47–53, April, 1994.

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Marinov, A.V. Stability estimates of continuous selections for metric almost-projections. Math Notes 55, 367–371 (1994). https://doi.org/10.1007/BF02112475

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