High Order Approximation by Multivariate Sublinear and Max-Product Operators

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


Here we study quantitatively the approximation of multivariate function by general multivariate positive sublinear operators with applications to multivariate Max-product operators. These are of Bernstein type, of Favard–Sz ász–Mirakjan type, of Baskakov type, of sampling type, of Lagrange interpolation type and of Hermite–Fejér interpolation type. Our results are both: under the presence of smoothness and without any smoothness assumption on the function to be approximated. It follows (Anastassiou, Approximation by Multivariate Sublinear and Max-Product Operators, 2017, submitted, [4]).


  1. 1.
    G. Anastassiou, Moments in Probability and Approximation Theory, Pitman Research Notes in Mathematics Series (Longman Group, New York, 1993)Google Scholar
  2. 2.
    G. Anastassiou, Approximation by Sublinear Operators (2017, submitted)Google Scholar
  3. 3.
    G. Anastassiou, Approximation by Max-Product Operators (2017, submitted)Google Scholar
  4. 4.
    G. Anastassiou, Approximation by Multivariate Sublinear and Max-Product Operators (2017, submitted)Google Scholar
  5. 5.
    B. Bede, L. Coroianu, S. Gal, Approximation by Max-Product Type Operators (Springer, Heidelberg, 2016)Google 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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