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Nonlinear approximation in N-dimension with the help of summability methods

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this paper, we approximate to functions in N-dimension by means of nonlinear integral operators of the convolution type. Our approximation is based on not only the uniform norm but also the variation semi-norm in Tonelli’s sense. We also study the rates of convergence. To get more general results we mainly use regular summability methods in the approximation. We construct some significant applications including the Cesàro approximation, the almost approximation, the rates of convergence based on certain summability methods. Furthermore, we display some graphical illustrations verifying the approximation and evaluate numerical computations giving approximation errors.

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Acknowledgements

The authors would like to thank the anonymous reviewer(s) for providing insightful comments and reading the manuscript carefully.

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Authors and Affiliations

  1. Department of Mathematics, Hacettepe University, Çankaya, 06800, Ankara, TR, Turkey

    Ismail Aslan

  2. Department of Mathematics, TOBB Economics and Technology University, Söğütözü, 06530, Ankara, TR, Turkey

    Oktay Duman

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  1. Ismail Aslan
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  2. Oktay Duman
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Correspondence to Ismail Aslan.

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Aslan, I., Duman, O. Nonlinear approximation in N-dimension with the help of summability methods. RACSAM 115, 105 (2021). https://doi.org/10.1007/s13398-021-01046-y

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