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An estimate on the convergence of MKZ–Bézier operators

✍ Scribed by Xiao-Ming Zeng; Bo-Yong Lian

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
372 KB
Volume
56
Category
Article
ISSN
0898-1221

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✦ Synopsis

The pointwise approximation properties of the MKZ-Bézier operators M n,α (f , x) for α ≥ 1 have been studied in [X.M. Zeng, Rates of approximation of bounded variation functions by two generalized Meyer-König-Zeller type operators, Comput. Math. Appl. 39 (2000) 1-13].

The aim of this paper is to study the pointwise approximation of the operators M n,α (f , x) for the other case 0 < α < 1. By means of some new estimate techniques and a result of Guo and Qi [S. Guo, Q. Qi, The moments for the Meyer-König and Zeller operators, Appl. Math. Lett. 20 (2007) 719-722], we establish an estimate formula on the rate of convergence of the operators M n,α (f , x) for the case 0 < α < 1.

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