Abstract
Here we study the approximation of functions by positive sublinear operators under differentiability. We produce general Jackson type inequalities under initial conditions. We apply these to a series of well-known Max-product operators. So our approach is quantitative by producing inequalities with their right hand sides involving the modulus of continuity of a high order derivative of the function under approximation. It follows Anastassiou, Coroianu, Gal (J. Comput. Anal. Appl. 12(2):396–406, 2010, [3]).
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Anastassiou, G.A. (2018). Approximation by Positive Sublinear Operators. In: Nonlinearity: Ordinary and Fractional Approximations by Sublinear and Max-Product Operators. Studies in Systems, Decision and Control, vol 147. Springer, Cham. https://doi.org/10.1007/978-3-319-89509-3_1
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DOI: https://doi.org/10.1007/978-3-319-89509-3_1
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