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Die Gute der \(L_p\)-Approximation durch Kantorovic-Polynome. (German) Zbl 0322.41012


MSC:

41A25 Rate of convergence, degree of approximation
41A10 Approximation by polynomials
41A35 Approximation by operators (in particular, by integral operators)
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References:

[1] Bojani?, R., Shisha, O.: Degree ofL 1-approximation to integrable functions by modified Bernstein polynomials. J. Approximation Theory13, 66-72 (1975) · Zbl 0305.41009 · doi:10.1016/0021-9045(75)90015-5
[2] Butzer, P. L., Berens, H.: Semi-Groups of Operators and Approximation, Berlin-Heidelberg-New York: Springer 1967 · Zbl 0164.43702
[3] Grundmann, A.: Güteabschätzungen für den Kantorovi?-Operator in derL 1-Norm. Math. Z.150, 45-47 (1976) · Zbl 0327.41016 · doi:10.1007/BF01213884
[4] Hoeffding, W.: TheL 1-Norm of the approximation error for Bernstein-type polynomials. J. Approximation Theory4, 347-356 (1971) · Zbl 0222.41010 · doi:10.1016/0021-9045(71)90001-3
[5] Johnen, H.: Inequalities connected with the moduli of smoothness. Mat. Vestnik, n. Ser.9, 289-303 (1972) · Zbl 0254.26005
[6] Kantorovi?, L. V.: Sur certains développements suivant les polynômes de la forme de S. Bernstein I, II. C. R. Acad. Sci. URSS, 563-568, 595-600 (1930) · JFM 57.1393.02
[7] Lorentz, G. G.: Bernstein Polynomials. Toronto. University of Toronto Press 1953
[8] Maier, V.: Güte- und Saturationsaussagen für dieL 1-Approximation durch spezielle Folgen linearer positiver Operatoren. Dissertation, Universität Dortmund 1976
[9] Peetre, J.: A theory of interpolation of normed spaces. Lecture Notes, Brazilia 1963 · Zbl 0162.44502
[10] Whitney, H.: Analytic extensions of differentiable functions defined in closed sets. Trans. Amer. math. Soc.36, 63-89 (1934) · Zbl 0008.24902 · doi:10.1090/S0002-9947-1934-1501735-3
[11] Zygmund, A.: Trigonometric series. Vol. I and II. London-New York: Cambridge University Press 1968 · Zbl 0157.38204
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