On better approximation order for the nonlinear Bleimann-Butzer-Hahn operator of maximum product kind

Document Type : Original Article

Authors

Sezin Cit

Ogun Doğru

Department of Mathematics, Faculty of Science, Gazi University, Turkey

10.22034/kjm.2023.357068.2641

Abstract

Using maximum instead of sum, nonlinear Bleimann-Butzer-Hahn operator of maximum product kind was introduced. The present paper deals with the approximation processes for this operator. In a previous study, it was indicated that the order of approximation of this operator to the function f under the modulus is $((x+1)^{(3/2)}√x)/(√n)$ and it could not be improved except for some subclasses of functions. Contrary to this claim, under some special conditions, we will show that a better order of approximation can be obtained with the help of classical and weighted modulus of continuities.

Keywords

Bleimann-Butzer-Hahn operators (BBH)

weighted modulus of continuity

nonlinear maximum product type operators

Subjects

• 41 Approximations and expansions

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