Sezin Çit, Ogün Doğru, On better approximation order for the nonlinear Baskakov operator of maximum product kind, Vol. 2025 (2025), Article ID 41, pp. 1-19

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DOI: 10.23952/cot.2025.41

Received April 7, 2024; Accepted August 21, 2024; Published online September 10, 2025

Abstract. The nonlinear Baskakov operator of the max-product type, which uses the maximum instead of the sum, was introduced by Bede et al. [8]. Our aim in this paper is to obtain a better approximation order for this operator. In [8], the approximation order for this operator was found to be $\frac{\sqrt{x\left( 1+x\right) }}{\sqrt{n}}$ with the help of the classical modulus of continuity, and it was claimed that this approximation order cannot be improved except for some subclasses of functions. Contrary to this claim, under some circumstances, we show that a better order of approximation can be obtained with the help of classical and weighted modulus of continuities.

How to Cite this Article:
S. Çit, O. Doğru, On better approximation order for the nonlinear Baskakov operator of maximum product kind, Commun. Optim. Theory 2025 (2025) 41.