High Order Approximation by Multivariate Sublinear and Max-Product Operators Under Convexity

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


Here we search quantitatively under convexity 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-Szász-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 which fulfills a convexity assumption. It follows (Anastassiou, Approximations by multivariate sublinear and max-product operators under convexity, submitted, 2017, [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, Approximations by Multivariate Sublinear and Max-product Operators under Convexity (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

Personalised recommendations