On Better Approximation Order for the Nonlinear Bernstein Operator of Maximum Product Kind

Abstract

Using maximum instead of sum, nonlinear Bernstein operator of maximum product kind is introduced by Bede et al. [2]. The present paper deals with the approximation processes for this operator. The order of approximation for this operator to the function f, can be found in [4] by means of the classical modulus of continuity. Also, in [4], it was indicated that the order of approximation of this operator to the function f under the modulus is 1/√n and it could not be improved except for some subclasses of functions. Contrary to this claim, in this paper, we will show that a better order of approximation can be obtained with the help of modulus of continuity.