An estimate on the convergence of MKZBzier operators
The pointwise approximation properties of the MKZBzier operators Mn,?(f,x) M n , ? ( f , x ) for ??1 ? ? 1 have been studied in [X.M. Zeng, Rates of approximation of bounded variation functions by two generalized MeyerKnigZeller type operators, Comput. Math. Appl. 39 (2000) 113]. The aim of this paper is to study the pointwise approximation of the operators Mn,?(f,x) M n , ? ( f , x ) for the other case 0<?<1 0 < ? < 1 . By means of some new estimate techniques and a result of Guo and Qi [S. Guo, Q. Qi, The moments for the MeyerKnig and Zeller operators, Appl. Math. Lett. 20 (2007) 719722], we establish an estimate formula on the rate of convergence of the operators Mn,?(f,x) M n , ? ( f , x ) for the case 0<?<1 0 < ? < 1 .
mkzbzier operators pointwise approximation rate of convergence lebesguestieltjes integral hlder inequality