# Pointwise approximation by Meyer-König and Zeller operators

Annales Polonici Mathematici (2000)

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

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topZeng, 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

top- [1] U. Abel, The moments for the Meyer-König and Zeller operators, J. Approx. Theory 82 (1995), 352-361. Zbl0828.41009
- [2] J. A. H. Alkemade, The second moment for the Meyer-König and Zeller operators, ibid. 40 (1984), 261-273. Zbl0575.41013
- [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] 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] E. W. Cheney and A. Sharma, Bernstein power series, Canad. J. Math. 16 (1964), 241-252. Zbl0128.29001
- [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] W. Feller, An Introduction to Probability Theory and Its Applications, Wiley, New York, 1971. Zbl0219.60003
- [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] 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] A. N. Shiryayev, Probability, Springer, New York, 1984.
- [11] V. Totik, Approximation by Meyer-König and Zeller type operators, Math. Z. 182 (1983), 425-446. Zbl0502.41006
- [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] 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] 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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