MKZ Type Operators Providing a Better Estimation on $[1/2,1)$

http://dx.doi.org/10.4153/CMB-2007-042-8
Canad. Math. Bull. 50(2007), 434-439

  Published:2007-09-01
 Printed: Sep 2007

In the present paper, we introduce a modification of the Meyer-K\"{o}nig and Zeller (MKZ) operators which preserve the test functions $f_{0}(x)=1$ and $f_{2}(x)=x^{2}$, and we show that this modification provides a better estimation than the classical MKZ operators on the interval $[\frac{1}{2},1)$ with respect to the modulus of continuity and the Lipschitz class functionals. Furthermore, we present the $r-$th order generalization of our operators and study their approximation properties.