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]).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
G. Anastassiou, Moments in Probability and Approximation Theory, Pitman Research Notes in Mathematics Series (Longman Group, New York, 1993)
G. Anastassiou, Intelligent Computations: Abstract Fractional Calculus, Inequalities, Approximations (Springer, Heidelberg, 2018)
G. Anastassiou, Approximation by Sublinear Operators (2017, submitted)
G. Anastassiou, L. Coroianu, S. Gal, Approximation by a nonlinear Cardaliagnet–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, Heidelberg, 2016)
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)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-89509-3_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-89508-6
Online ISBN: 978-3-319-89509-3
eBook Packages: EngineeringEngineering (R0)