Abstract
In this paper, we investigate the simultaneous approximation of Bernstein-Sikkema operators, and establish the direct and equivalent theorems by using the Ditzian-Totik modulus of smoothness.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ditzian, Z., Direct Estimates for Bernstein Polynomials, J. of Approx. Theory, 79(1994), 165–166.
Li, S., The Direct and Inverse Theorems for Bernstein-Sikkema Operators, J. of Appl.d Math., 1:19(1996), 144–148.
Xiong, Q. L. and Cao, F. L., Approximation of Bernstein-Sikkema Operators, J. of Appl. Math. Res. and Exposition, 19(1999), 261–265.
Li, C. X. and Liu, Y. Approximation of Bernstein-Sikkema Operators and Their Derivatives, J. of Hebei Normal University, 3:30(2006), 249–252.
Ditzian, Z., Totik V., Moduli of Smoothness, New York: Spring-Verlag, 1987.
Xu, C. N. and He, J. X., Derivative Approximation by Sikkema-Bernstein Operators, J. of Mathematic Research and Exposition, 1:14(1994),153–154.
Jiang, H. B. and Xie, L. S., Simultaneous Approximation of Bernstein Operators, Pure and Applied Mathematics, 4:22(2006), 471–476.
Zhou, D. X., On Smoothness Characterized by Bernstein-type Operator, J. of Approximation Theory, 81(1995), 303–315.
Ditzian, Z., A Global Inverse Theorem for Combinations of Bernstein Polynomials, J. of Approximation Theory, 26(1979), 277–292.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the National Natural Science Foundation of China (10631080) and the Zhejiang Provincial Key Basic Subject Foundation of China(10571014).
Rights and permissions
About this article
Cite this article
Jiang, X., Xie, L. Simultaneous approximation by Bernstein-Sikkema operators. Anal. Theory Appl. 24, 237–246 (2008). https://doi.org/10.1007/s10496-008-0237-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10496-008-0237-7