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.