On better approximation order for the nonlinear Bernstein operator of maximum product kind

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 root 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.