Pointwise approximation by Meyer-König and Zeller operators

Xiao-Ming Zeng; Jun-Ning Zhao

Annales Polonici Mathematici (2000)

  • Volume: 73, Issue: 2, page 185-196
  • ISSN: 0066-2216

Abstract

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We study the rate of pointwise convergence of Meyer-König and Zeller operators for bounded functions, and get an asymptotically optimal estimate.

How to cite

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Zeng, Xiao-Ming, and Zhao, Jun-Ning. "Pointwise approximation by Meyer-König and Zeller operators." Annales Polonici Mathematici 73.2 (2000): 185-196. <http://eudml.org/doc/262531>.

@article{Zeng2000,
abstract = {We study the rate of pointwise convergence of Meyer-König and Zeller operators for bounded functions, and get an asymptotically optimal estimate.},
author = {Zeng, Xiao-Ming, Zhao, Jun-Ning},
journal = {Annales Polonici Mathematici},
keywords = {asymptotically optimal; rate of convergence; basis functions and moments of approximation operators; Meyer-König operators; Zeller operators},
language = {eng},
number = {2},
pages = {185-196},
title = {Pointwise approximation by Meyer-König and Zeller operators},
url = {http://eudml.org/doc/262531},
volume = {73},
year = {2000},
}

TY - JOUR
AU - Zeng, Xiao-Ming
AU - Zhao, Jun-Ning
TI - Pointwise approximation by Meyer-König and Zeller operators
JO - Annales Polonici Mathematici
PY - 2000
VL - 73
IS - 2
SP - 185
EP - 196
AB - We study the rate of pointwise convergence of Meyer-König and Zeller operators for bounded functions, and get an asymptotically optimal estimate.
LA - eng
KW - asymptotically optimal; rate of convergence; basis functions and moments of approximation operators; Meyer-König operators; Zeller operators
UR - http://eudml.org/doc/262531
ER -

References

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  1. [1] U. Abel, The moments for the Meyer-König and Zeller operators, J. Approx. Theory 82 (1995), 352-361. Zbl0828.41009
  2. [2] J. A. H. Alkemade, The second moment for the Meyer-König and Zeller operators, ibid. 40 (1984), 261-273. Zbl0575.41013
  3. [3] M. Becker and R. J. Nessel, A global approximation theorem for the Meyer-König and Zeller operators, Math. Z. 160 (1978), 195-206. Zbl0376.41007
  4. [4] R. Bojanic and M. Vuilleumier, On the rate of convergence of Fourier-Legendre series of functions of bounded variation, J. Approx. Theory 31 (1981), 67-79. Zbl0494.42003
  5. [5] E. W. Cheney and A. Sharma, Bernstein power series, Canad. J. Math. 16 (1964), 241-252. Zbl0128.29001
  6. [6] F. Cheng, On the rate of convergence of Bernstein polynomials of functions of bounded variation, J. Approx. Theory 39 (1983), 259-274. Zbl0533.41020
  7. [7] W. Feller, An Introduction to Probability Theory and Its Applications, Wiley, New York, 1971. Zbl0219.60003
  8. [8] S. Guo and M. Khan, On the rate of convergence of some operators on functions of bounded variation, J. Approx. Theory 58 (1989), 90-101. Zbl0683.41030
  9. [9] V. Maier, M. W. Müller and J. Swetits, L₁ saturation class of the integrated Meyer-König and Zeller operators, ibid. 32 (1981), 27-31. Zbl0489.41022
  10. [10] A. N. Shiryayev, Probability, Springer, New York, 1984. 
  11. [11] V. Totik, Approximation by Meyer-König and Zeller type operators, Math. Z. 182 (1983), 425-446. Zbl0502.41006
  12. [12] X. M. Zeng, Bounds for Bernstein basis functions and Meyer-König and Zeller basis functions, J. Math. Anal. Appl. 219 (1998), 364-376. Zbl0909.41015
  13. [13] X. M. Zeng, On the rate of convergence of the generalized Szász type operators for bounded variation functions, ibid. 226 (1998), 309-325. Zbl0915.41016
  14. [14] X. M. Zeng and A. Piriou, On the rate of convergence of two Bernstein-Bézier type operators for bounded variation functions, J. Approx. Theory 95 (1998), 369-387. Zbl0918.41016

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