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

Abstract In the present paper, we introduce a modification of the Meyer-König and Zeller $\left( \text{MKZ} \right)$ operators which preserve the test functions ${{f}_{0}}\left( x \right)=1$ and ${{f}_{2}}\left( x \right)={{x}^{2}}$ , and we show that this modification provides a better estimation than the classical $\left( \text{MKZ} \right)$ operators on the interval $\left[ \frac{1}{2},1 \right)$ 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.