Canavati Fractional Approximations Using Max-Product Operators

  • George A. Anastassiou
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 147)


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]).


  1. 1.
    G. Anastassiou, Fractional Differentiation Inequalities (Springer, New York, 2009)CrossRefGoogle Scholar
  2. 2.
    G. Anastassiou, Intelligent Mathematics: Computational Analysis (Springer, New York, 2011)CrossRefGoogle Scholar
  3. 3.
    G. Anastassiou, Canavati Fractional Approximation by Max-product Operators. Progress in Fractional Differentiation and Applications (2017)Google Scholar
  4. 4.
    G. Anastassiou, Caputo Fractional Approximation by Sublinear Operators (2017, submitted)Google Scholar
  5. 5.
    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)MathSciNetzbMATHGoogle Scholar
  6. 6.
    B. Bede, L. Coroianu, S. Gal, Approximation by Max-Product Type Operators (Springer, New York, 2016)CrossRefGoogle Scholar
  7. 7.
    J.A. Canavati, The Riemann-Liouville integral. Nieuw Archif Voor Wiskunde 5(1), 53–75 (1987)MathSciNetzbMATHGoogle Scholar
  8. 8.
    R.A. DeVore, G.G. Lorentz, Constructive Approximation (Springer, Berlin, 1993)CrossRefGoogle Scholar
  9. 9.
    L. Fejér, Über Interpolation. Göttingen Nachrichten (1916), pp. 66–91Google Scholar
  10. 10.
    G.G. Lorentz, Bernstein Polynomials, 2nd edn. (Chelsea Publishing Company, New York, 1986)Google Scholar
  11. 11.
    T. Popoviciu, Sur l’approximation de fonctions convexes d’order superieur. Mathematica (Cluj) 10, 49–54 (1935)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of MemphisMemphisUSA

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