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Demonstratio Mathematica

Editor-in-Chief: Vetro, Calogero

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CiteScore 2018: 0.47
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Source Normalized Impact per Paper (SNIP) 2018: 0.714

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Volume 51, Issue 1


Approximations by multivariate sublinear and Max-product operators under convexity

George A. Anastassiou
Published Online: 2018-05-30 | DOI: https://doi.org/10.1515/dema-2018-0008


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.

Keywords: multivariate positive sublinear operators; multivariate Max-product operators; multivariate modulus of continuity; convexity

MSC 2010: 41A17; 41A25; 41A36; 41A63


  • [1] Bede B., Coroianu L., Gal S., Approximation by Max-Product type Operators, Springer, Heidelberg, New York, 2016Google Scholar

  • [2] Anastassiou G., Moments in probability and approximation theory, Pitman Research Notes in Mathematics Series, Longman Group UK, New York, NY, 1993Google Scholar

  • [3] Anastassiou G., Approximation by Sublinear Operators, submitted, 2017Google Scholar

  • [4] Anastassiou G., Approximation by Max-Product Operators, submitted, 2017Google Scholar

About the article

Received: 2017-11-06

Accepted: 2018-04-06

Published Online: 2018-05-30

Citation Information: Demonstratio Mathematica, Volume 51, Issue 1, Pages 85–105, ISSN (Online) 2391-4661, DOI: https://doi.org/10.1515/dema-2018-0008.

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© 2018 George A. Anastassiou. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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