WEIGHTED APPROXIMATION IN UNIFORM NORM BY MEYER-K¨ONIG AND ZELLER OPERATORS

Abstract

The weighted approximation errors of $Meyer-K\ddot{o}nig$ and $Zeller$ operator is characterized for weights of the form $w(x) = x^{\gamma_0}(1 − x)^{\gamma_1} $, where $\gamma_0 \in [−1, 0], \gamma_1 \in \mathbb{R}$. Direct inequalities and strong converse inequalities of type A are proved in terms of the weighted $K$-functional.