Abstract
Here we study the approximation of functions by sublinear positive operators with applications to a large variety of Max-Product operators under Canavati fractional differentiability. Our approach is based on our general fractional results about positive sublinear operators. We derive Jackson type inequalities under simple initial conditions. So our way is quantitative by producing inequalities with their right hand sides involving the modulus of continuity of Canavati fractional derivative of the function under approximation. It follows Anastassiou (Canavati fractional approximation by max-product operators. Progress in fractional differentiation and applications, 2017, [3]).
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References
G. Anastassiou, Fractional Differentiation Inequalities (Springer, New York, 2009)
G. Anastassiou, Intelligent Mathematics: Computational Analysis (Springer, New York, 2011)
G. Anastassiou, Canavati Fractional Approximation by Max-product Operators. Progress in Fractional Differentiation and Applications (2017)
G. Anastassiou, Caputo Fractional Approximation by Sublinear Operators (2017, submitted)
G. Anastassiou, L. Coroianu, S. Gal, Approximation by a nonlinear Cardaliaguet-Euvrard neural network operator of max-product kind. J. Comput. Anal. Appl. 12(2), 396–406 (2010)
B. Bede, L. Coroianu, S. Gal, Approximation by Max-Product Type Operators (Springer, New York, 2016)
J.A. Canavati, The Riemann-Liouville integral. Nieuw Archif Voor Wiskunde 5(1), 53–75 (1987)
R.A. DeVore, G.G. Lorentz, Constructive Approximation (Springer, Berlin, 1993)
L. Fejér, Über Interpolation. Göttingen Nachrichten (1916), pp. 66–91
G.G. Lorentz, Bernstein Polynomials, 2nd edn. (Chelsea Publishing Company, New York, 1986)
T. Popoviciu, Sur l’approximation de fonctions convexes d’order superieur. Mathematica (Cluj) 10, 49–54 (1935)
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Anastassiou, G.A. (2018). Canavati Fractional Approximations Using Max-Product 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_5
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DOI: https://doi.org/10.1007/978-3-319-89509-3_5
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