Pointwise Weighted Approximation of Functions with Endpoint Singularities by Combinations of Bernstein Operators

Lu Wenming

Abstract


We give direct and inverse theorems for the weighted approximation of functions with endpoint singularities by combinations of Bernstein operators.


Keywords


Combinations of Bernstein polynomials; Functions with endpoint singularities; Direct and inverse results.

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References


P.L. Butzer, Linear combinations of Bernstein polynomials, Canad. J. Math. 5 (1953), pp. 559-567.

H. Berens and G. Lorentz, Inverse theorems for Bernstein polynomials, Indiana Univ. Math. J. 21 (1972), pp. 693-708.

D. Della Vechhia, G. Mastroianni and J. Szabados, Weighted approximation of functions with endpoint and inner singularities by Bernstein operators, Acta Math. Hungar. 103 (2004), pp. 19-41.

Z. Ditzian, A global inverse theorem for combinations of Bernstein polynomials, J. Approx. Theory 26 (1979), pp. 277-292.

Z. Ditzian and V. Totik, Moduli of Smoothness, Springer-Verlag, Berlin, New York (1987).

S.S. Guo, C.X. Li and X.W. Liu, Pointwise approximation for linear combinations o Bernstein operators, J. Approx. Theory 107 (2000), pp. 109-120.

S.S. Guo, H. Tong and G. Zhang, Pointwise weighted approximation by Bernstein operators, Acta Math. Hungar. 101 (2003), pp. 293-311.

G.G. Lorentz, Bernstein Polynomial, University of Toronto Press, Toronto (1953).

L.S. Xie, Pointwise simultaneous approximation by combinations of Bernstein operators, J. Approx. Theory 137 (2005), pp. 1-21.

L.S. Xie, The saturation class for linear combinations of Bernstein operators, Arch. Math. 91 (2008), pp. 86-96.

D.S. Yu,weighted approximation of functions with singularities by combinations of Bernstein operators, J.Applied Mathematics and Computation. 206(2008),pp.906-918.

D.S. Yu and D.J. Zhao, Approximation of functions with singularities by truncated Bernstein operators, Southeast Bull. Math. 30 (2006), pp. 1178-1189.

D.X. Zhou, Rate of convergence for Bernstein operators with Jacobi weights, Acta Math. Sinica 35 (1992), pp. 331-338.

D.X. Zhou, On smoothness characterized by Bernstein type operators, J. Approx. Theory 81 (1994), pp. 303-315.

J.J. Zhang, Z.B. Xu, Direct and inverse approximation theorems with Jacobi weight for combinations and higher derivatives of Baskakov operators(in Chinese), Journal of systems science and mathematical sciences. 2008 28 (1), pp. 30-39.


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