An estimate on the convergence of MKZ-Bezier operators
The point wise approximation properties of the MKZ-Bezier operators M(n,alpha)(f, x) for alpha >= 1 have been studied in [X.M. Zeng, Rates of approximation of bounded variation functions by two generalized Meyer-Konig-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,alpha)(f, x) for the other case 0 < alpha < 1. By means of some new estimate techniques and a result of Guo and Qi [S. Guo, Q. Qi, The moments for the Meyer-Konig 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,alpha)(f. x) for the case 0 < alpha < 1. (c) 2008 Elsevier Ltd. All rights reserved.
mkz-bezier operators pointwise approximation rate of convergence lebesgue-stieltjes integral holder inequality