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Results in Mathematics

, 74:201 | Cite as

Fejér Sums and Chebyshev Polynomials

  • Jorge Bustamante
  • Juan Jesús Merino-García
  • José María QuesadaEmail author
Article
  • 78 Downloads

Abstract

Let \(L^p_w[-1,1]\) be the weighted Lebesgue space on \([-1,1]\) with \(w(t)=(1-t^2)^{-1/2}\). We prove that the rate of convergence in \(L^p_w[-1,1]\) of the Fejér sums is equivalent to a fractional modulus of smoothness of order 1/2.

Keywords

Polynomial approximation Chebyshev polynomials Fejér operators direct results strong converse results fractional moduli of smoothness 

Mathematics Subject Classification

41A410 41A425 41A435 41A436 

Notes

Acknowledgements

The last author is partially supported by Research Project PGC2018-097621-B-I00 and by Junta de Andalucía, Research Group FQM268.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Facultad de Ciencias Físico-MatemáticasBenemérita Universidad Autónoma de PueblaPueblaMexico
  2. 2.Department of MathematicsUniversity of JaénJaénSpain

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