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The Simultaneous Approximation Average Errors for Bernstein Operators on the r-Fold Integrated Wiener Space

Published online by Cambridge University Press:  28 May 2015

Guiqiao Xu
Guiqiao Xu*
Affiliation:
Department of Mathematics, Tianjin Normal University, Tianjin, 300387, China
*
*Corresponding author.Email address:Xuguiqiao@eyou.com
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Abstract

For weighted approximation in Lp-norm, we determine strongly asymptotic orders for the average errors of both function approximation and derivative approximation by the Bernstein operators sequence on the r-fold integrated Wiener space.

Keywords

41A2865D0541A25Bernstein operatorsweighted Lp-normr-fold integrated Wiener spaceaverage error
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 5 , Issue 3 , August 2012 , pp. 403 - 422
Copyright
Copyright © Global Science Press Limited 2012

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References

[1]Traub, J. F., Wasilkowski, G. W., Wozźniakowski, H., Information-Based Complexity, Academic Press, New York, 1988.Google Scholar
[2]Ritter, K., Approximation and Optimization on the Wiener Space, J. Complexity, 6(1990), pp. 337–364.CrossRefGoogle Scholar
[3]Hickernell, F. J., Woźniakowski, H., Integration and approximation in arbitrary dimensions, Adv. Comput. Math., 12(2000), pp. 25–58.CrossRefGoogle Scholar
[4]Kon, M., Plaskota, L., Information-based nonlinear approximation: an average case setting, J. Complexity, 21(2005), pp. 211–229.CrossRefGoogle Scholar
[5]Ritter, K., Average-case analysis of numerical problems, Springer-Verlag, New York, 2000.Google Scholar
[6]Xu, G. Q., Du, Y. F., The Average Errors for Hermite-Fejéer Interpolation on the Wiener Space, Science in China Series A, Mathematics, 53(6)(2010), pp. 1841–1852.CrossRefGoogle Scholar
[7]Lorentz, G. G., Bernstein Polynomials, Univ. of Toronto, 1953.Google Scholar
[8]Devore, R. A., Lorentz, G. G., Constructive Approximation, Springer-Verlag, Berlin, 1993.CrossRefGoogle Scholar
[9]SunY. S, Y. S,, Wang, C. Y., Average error bounds of best approximation of continuous functions on the Wiener space, J. Complexity, 11(1995), pp. 74–104.CrossRefGoogle Scholar