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Mixed Conformable Fractional Approximation Using Positive Sublinear Operators

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

Abstract

Here we consider the approximation of functions by positive sublinear operators with applications to a large variety of Max-Product operators under mixed conformable fractional differentiability. These are examples of positive sublinear operators. Our study is based on our general results about positive sublinear operators. We produce Jackson type inequalities under mixed conformable related basic initial conditions. So our approach is quantitative by producing inequalities with their right hand sides involving the modulus of continuity of a high order mixed conformable fractional derivative of the function under approximation. It follows Anastassiou, (Mixed Conformable Fractional Approximation by Sublinear Operators, 2017), [3]).

References

  1. 1.
    T. Abdeljawad, On conformable fractional calculus. J. Comput. Appl. Math. 279, 57–66 (2015)MathSciNetCrossRefGoogle Scholar
  2. 2.
    G. Anastassiou, Approximation by Sublinear Operators (2017), (submitted)Google Scholar
  3. 3.
    G. Anastassiou, Mixed Conformable Fractional Approximation by Sublinear Operators 2017, (submitted)Google Scholar
  4. 4.
    B. Bede, L. Coroianu, S. Gal, Approximation by Max-Product type Operators (Springer, Heidelberg, New York, 2016)CrossRefGoogle Scholar
  5. 5.
    L. Fejér, Über Interpolation, Göttingen Nachrichten (1916), pp. 66–91Google Scholar
  6. 6.
    R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)Google Scholar
  7. 7.
    G.G. Lorentz, Bernstein Polynomials, 2nd edn (Chelsea Publishing Company, New York, NY, 1986)Google Scholar
  8. 8.
    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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