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Quantitative Korovkin type theorems on simultaneous approximation

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References

  1. Brudnyî, Yu.A.: On a certain method for approximation of bounded functions, given on a segment (Russian). In: Studies Contemporary Problems Constructive Theory of Functions (Proc. Second All-Union Conf., Baku 1962; ed. by I.I. Ibragimov), pp. 40–45. Baku: Izdat. Akad. Nauk Azerbaidžan. 1965

    Google Scholar 

  2. DeVore, R.A.: The Approximation of Continuous Functions by Positive Linear Operators. Berlin-Heidelberg-New York: Springer 1972

    Google Scholar 

  3. Freud, G.: On approximation by positive linear methods, II. Studia Sci. Math. Hungar.3, 365–370 (1968)

    Google Scholar 

  4. Gonska, H.H., Meier, J.: A bibliography on approximation of functions by Bernstein type operators (1955–1982). In: Approximation Theory IV (Proc. Int. Sympos. College Station 1983; ed by C.K. Chui, L.L. Schumaker, J.D. Ward), pp. 739–785. New York-San Francisco-London: Academic Press 1984

    Google Scholar 

  5. Ivan, M., Gavrea, I.: Sur une suite d'opérateurs d'interpolation et d'approximation. Anal. Numér. Theor. Approx. (2)10, 187–189 (1981)

    Google Scholar 

  6. Kansy, K.: Elementare Fehlerabschätzungen für Ableitungen bei der Hermite-Interpolation. Numer. Math.21, 350–354 (1973)

    Google Scholar 

  7. Kelisky, R.P., Rivlin, T.J.: Iterates of Bernstein Polynomials. Pacific J. Math.21, 511–520 (1967)

    Google Scholar 

  8. Knoop, H.-B., Pottinger, P.: Ein Satz vom Korovkin-Typ fürC k-Räume. Math. Z.148, 23–32 (1976)

    Google Scholar 

  9. Kudrjavcev, G.I.: Convergence of sequences of linear operators to derivatives (Russian). In: Proc. Central Regional Union of Mathematics Departments, No. 1: Functional Analysis and Function Theory, pp. 122–136. Kalinin: Kalinin. Gos. Ped. Inst. 1970

    Google Scholar 

  10. Kudrjavcev, G.I.: On the order of approximation by some sequences of operators of class M (Russian). Naučn. Tr. Novosib. Gos. Ped. Inst.94, 20–23 (1974)

    Google Scholar 

  11. Lorentz, G.G.: Zur Theorie der Polynome von S. Bernstein. Mat. Sb. (N.S.)2, 543–556 (1937)

    Google Scholar 

  12. Lorentz, G.G.: Bernstein Polynomials. Toronto: University of Toronto Press 1953

    Google Scholar 

  13. Min'kova, R.M.: The convergence of the derivatives of linear operators (Russian). C.R. Acad. Bulgare Sci.23, 627–629 (1970)

    Google Scholar 

  14. Min'kova, R.M.: Convergence of derivatives of linear operators (Russian). Izv. Vysš. Učebn. Zaved. Matematika no. 8 (171), 52–59 (1976)

    Google Scholar 

  15. Moldovan, G.: Asupra aproximârii funcţiilor continue prin polinoame Bernstein. Studia Univ. Babeş-Bolyai Ser. Math.-Phys. (1)11, 63–71 (1966)

    Google Scholar 

  16. Popoviciu, T.: Despre cea mai bunâ aproximaţie a funcţiilor continue prin polinoame. Cluj: Inst. Arte Grafice 1937

    Google Scholar 

  17. Pottinger, P.: Zur linearen Approximation im RaumeC k(I). Habilitationsschrift, Universität Duisburg 1976

  18. Sakai, R.: Approximation problem restricted by an incidence matrix. J. Math. Soc. Japan (3)32, 557–585 (1980)

    Google Scholar 

  19. Sendov, Bl., Popov, V.A.: The convergence of the derivatives of positive linear operators (Russian). C.R. Acad. Bulgare Sci.22, 507–509 (1969)

    Google Scholar 

  20. Sendov, Bl., Popov, V.A.: Convergence of the derivatives of positive linear operators (Bulgarian). Bulgar. Akad. Nauk., Otd. Mat. Fiz. Nauki, Izv. Mat. Inst.11, 107–115 (1970)

    Google Scholar 

  21. Shisha, O., Mond, B.: The degree of convergence of linear positive operators. Proc. Nat. Acad. Sci. U.S.A.60, 1196–1200 (1968)

    Google Scholar 

  22. Stancu, D.D.: Quadrature formulas constructed by using certain linear positive operators. In: Numerische Integration (Proc. Conf. Math. Res. Inst. Oberwolfach 1981; ed. by G. Hämmerlin), pp. 241–251. Basel: Birkhäuser 1982

    Google Scholar 

  23. Stark, E.L.: Bernstein-Polynome, 1912–1955. In: Functional Analysis and Approximation (Proc. Conf. Math. Res. Inst. Oberwolfach 1980; ed. by P. Butzer, B. Sz.-Nagy, E. Görlich), pp. 443–461. Basel: Birkhäuser 1981

    Google Scholar 

  24. Stark, E.L.: 1. Nachtrag zu “Bernstein-Polynome, 1912–1955”. Written communication, March 1982

  25. Wigert, S.: Sur l'approximation par polynomes des fonctions continues. Ark. Mat. Astr. Fys.22B, 1–4 (1932)

    Google Scholar 

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  1. Department of Mathematics, University of Duisburg, Lotharstraße 65, D-4100, Duisburg 1, Federal Republic of Germany

    Heinz H. Gonska

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  1. Heinz H. Gonska
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Gonska, H.H. Quantitative Korovkin type theorems on simultaneous approximation. Math Z 186, 419–433 (1984). https://doi.org/10.1007/BF01174895

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  • DOI: https://doi.org/10.1007/BF01174895

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