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Proceedings - Mathematical Sciences

, Volume 127, Issue 2, pp 361–374 | Cite as

Diliberto–Straus algorithm for the uniform approximation by a sum of two algebras

  • AIDA KH ASGAROVA
  • VUGAR E ISMAILOV
Article
  • 53 Downloads

Abstract

In 1951, Diliberto and Straus [5] proposed a levelling algorithm for the uniform approximation of a bivariate function, defined on a rectangle with sides parallel to the coordinate axes, by sums of univariate functions. In the current paper, we consider the problem of approximation of a continuous function defined on a compact Hausdorff space by a sum of two closed algebras containing constants. Under reasonable assumptions, we show the convergence of the Diliberto–Straus algorithm. For the approximation by sums of univariate functions, it follows that Diliberto–Straus’s original result holds for a large class of compact convex sets.

Keywords

Uniform approximation levelling algorithm proximity map bolt. 

Mathematics Subject Classifications:

41A30 41A65 46B28 65D15. 

Notes

Acknowledgement

The authors are grateful to the referee for numerous comments and suggestions that improved the original manuscript.

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Copyright information

© Indian Academy of Sciences 2017

Authors and Affiliations

  1. 1.Institute of Mathematics and MechanicsNational Academy of Sciences of AzerbaijanBakuAzerbaijan

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