Abstract
In this paper we give equivalent theorems on simultaneous approximation for the combinations of Bernstein operators by r-th Ditzian-Totik modulus of smoothness \(\omega _{\varphi ^\lambda }^r (f,t)(0 \leqslant \lambda \leqslant 1)\). We also investigate the relation between the derivatives of the combinations of Bernstein operators and the smoothness of derivatives of functions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ditzian, Z. and Totik, V., Moduli of Smoothness, Springer-Verlag, New York, 1987.
Zhou, D. X., On Smoothness Characterized by Bernstein-type Operators, J. Approx. Theory, 81(1995), 303–315.
Song, R. Y., Equivalence Theorem on Simultaneous Approximation by the Linear Combination of Bernstein type Operators, J. Zhejiang University, 27:1(2000), 35–41.
Xie, L. S. and Zhang, X. P., Pointwise Estimate on Simultaneous Approximation by Linear Combination of Bernstein Operators, Appl. Math. J. Chinese Univ. Ser A, 17:4(2002), 479–484.
Zhou, X. L., About Bernstein Operators, Acta Mathematica Sinica, 28:6(1985), 848–855.
Xie, L. S., About Steckin-Marchaud type Inequoters, J. Lishui Teachers College, 19(1997), 1–3.
Author information
Authors and Affiliations
Additional information
Supported by the Key Academic Discipline of Zhejiang Provincial of China under Grant No.2005.
Rights and permissions
About this article
Cite this article
Cheng, L., Xie, L. Equivalent theorems on simultaneous approximation by combinations of Bernstein operatores. Analys in Theo Applic 22, 246–253 (2006). https://doi.org/10.1007/s10496-006-0246-3
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10496-006-0246-3