, Volume 15, Issue 1, pp 11–16

Korovkin-type theorem for sequences of operators preserving shape



In the paper we present Korovkin-type theorem concerning conditions of convergence sequences of linear operators preserving shape.


Korovkin theorem Shape-preserving approximation 

Mathematics Subject Classification (2000)

Primary 41A35 Secondary 41A36 


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  1. 1.
    Shisha O.: Monotone approximation. Pac. J. Math. 15(2), 667–671 (1965)MATHMathSciNetGoogle Scholar
  2. 2.
    Lorentz G.G., Zeller K.L.: Monotone approximation by algebraic polynomials. Trans. Am. Soc. 149(1), 1–18 (1970)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    DeVore R.A., Yu X.M.: Pointwise estimates for monotone polynomial approximation. Constr. Approx. 1, 323–331 (1985)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Shvedov A.S.: Comonotone approximation of functions by polynomials. Sov. Math. Dokl. 21(1), 34–37 (1980)MATHMathSciNetGoogle Scholar
  5. 5.
    Shvedov A.S.: Orders of coapproximation of functions by algebraic polynomials. Math. Notes 29, 63–70 (1981)MATHMathSciNetGoogle Scholar
  6. 6.
    Newman D.J.: Efficient comonotone approximation. J. Approx. Theory 25, 189–192 (1979)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Beatson R.K., Leviatan D.: On comonotone approximation. Can. Math. Bull. 26, 220–224 (1983)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Leviatan, D.: In: Szabados, J., Tandori, K.: (eds.) Approximation and Function Series, pp. 63–84. Bolyai Society, Budapest (1996)Google Scholar
  9. 9.
    Leviatan D.: Shape-preserving approximation by polynomials. J. Comput. Appl. Math. 121, 73–94 (2000)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Gal S.G.: Shape-Preserving Approximation by Real and Complex Polynomials. Springer, New York (2008)MATHCrossRefGoogle Scholar
  11. 11.
    Korovkin, P.P.: On the order of approximation of functions by linear positive operators. Dokl. Akad. Nauk SSSR. 114(6), 1158–1161 (1957) (Russian)Google Scholar
  12. 12.
    Karlin, S., Stadden, W.: Tchebycheff systems: with applications in analysis and statistics. In: Pure and Applied Mathematics, vol. XV. Wiley, New York (1966)Google Scholar
  13. 13.
    Muñoz-Delgado F.J., Ramírez-González V., Cárdenas-Morales D.: Qualitative Korovkin-type results on conservative approximation. J. Approx. Theory 94, 144–159 (1998)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Department of Mechanics and MathematicsSaratov State UniversitySaratovRussian Federation

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