Acta Mathematica Hungarica
Volume/Issue:
Volume 135: Issue 1-2
Simultaneous approximation by combinations of Bernstein–Kantorovich operators
Authors: Li Cheng 1 and Linsen Xie 1
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  • 1 Department of Mathematics, Lishui University, Lishui 323000, Zhejiang Province, People's Republic of China
DOI:
https://doi.org/10.1007/s10474-011-0162-7
Page Count:
130–147
Publication Date:
01 Apr 2012
Online Publication Date:
06 Oct 2011
Article Category:
Research Article
Restricted access

Abstract.

We prove some new direct and converse results on simultaneous approximation by the combinations of Bernstein–Kantorovich operators using the Ditzian–Totik modulus of smoothness.

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  • [7] Guo, S. S. Liu, L. X. Qi, Q. L. 2002 Pointwise estimate for linear combinations of Bernstein–Kantorovich operators J. Math. Anal. Appl. 265 135–147 .

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  • [8] Guo, S. S. Li, C. X. Sun, Y. G. Yang, G. Yue, S. J. 1998 Pointwise estimate for Szász-type operators J. Approx. Theory 94 160–171 .

  • [9] Xie, L. S. Xie, T. F. 1999 A pointwise inverse theorem for combination of Bernstein polynomials Chinese J. Contemporary Math. 20 373–386.

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  • [10] Zhou, D. X. 1995 On smoothness characterized by Bernstein type operators J. Approx. Theory 81 303–315 .
Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632
Keywords:
simultanous approximation; moduli of smoothness; combination of Bernstein–Kantorovich operators; 41A36

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