An estimate on the convergence of MKZ–Bézier operators

The pointwise approximation properties of the MKZ–Bézier operators Mn,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 Mn,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 Mn,α(f,x) for the case 0<α<1.