Approximation by Sublinear Operators
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Abstract
Here we study the approximation of functions by positive sublinear operators under di¤erentiability. 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.
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Anastassiou, G.
(2018).
Approximation by Sublinear Operators.
Acta Mathematica Universitatis Comenianae, 87(2), 237-250.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/678/626
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References
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[3] G. Anastassiou, L. Coroianu, S. Gal, Approximation by a nonlinear Cardaliagnet-Euvrard neural network operator of max-product kind, J. Computational Analysis & Applications, Vol. 12, No. 2 (2010), 396-406.
[4] B. Bede, L. Coroianu, S. Gal, Approximation by Max-Product type Operators, Springer, Heidelberg, New York, 2016.
[5] G.G. Lorentz, Bernstein Polynomials, Chelsea Publishing Company, New ork, NY, 1986, 2nd edition.
[6] T. Popoviciu, Sur l'approximation de fonctions convexes d'order superieur, Mathematica (Cluj), 10 (1935), 49-54.