Higher Order Approximation of Continuous Functions by a Modified Meyer-K\"{o}nig and Zeller-Type Operator

Abstract

A new Goodman-Sharma type modification of the Meyer-K\"{o}nig and Zeller operator for approximation of bounded continuous functions on [0,1) is presented. We estimate the approximation error of the proposed operator and prove direct and strong converse theorems with respect to a related K-functional. The operator is linear but not a positive one. However it benefits a better order of approximation compared to the Goodman-Sharma variant of Meyer-K\"{o}nig and Zeller type operator investigated by Ivanov and Parvanov in 2012.