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

TL;DR

This paper improves the understanding of the approximation order of a nonlinear Baskakov operator of maximum product kind, showing that better approximation rates are achievable under certain conditions using classical and weighted moduli of continuity.

Contribution

The paper demonstrates that the approximation order of the nonlinear Baskakov operator can be improved beyond previous claims by employing classical and weighted moduli of continuity.

Findings

Enhanced approximation order with classical modulus

Improved approximation order with weighted modulus

Applicable to specific subclasses of functions

Abstract

Using maximum instead of sum, nonlinear Baskakov 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 under some circumstances, we will show that a better order of approximation can be obtained with the help of classical and weighted modulus of continuities.