On Better Approximation Order for the Nonlinear Meyer-K\"onig and Zeller Operator of Maximum Product Kind

Abstract

Using maximum instead of sum, nonlinear Meyer-K\"onig and Zeller operator of maximum product kind is introduced by Bede et al. The present paper deals with the approximation processes for this operator. Especially in, it was indicated that the order of approximation of this operator to the function f under the modulus is and it could not be improved except for some subclasses of functions. Contrary to this claim, we will show that a better order of approximation can be obtained with the help of classical modulus of continuity