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The Valleé-Poussin Means for Special Series With Respect to Ultraspherical Jacobi Polynomials With Sticking Partial Sums

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Abstract

The authors continue study of special series with sticking property (r-fold coincidence at points ± 1) in ultraspherical Jacobi polynomials, that was started in the previous works of the first author. In the present paper they are dealing with an approximative properties of Valleé-Poussin means for partial sums of the mentioned special series. It is shown that for function f with certain smoothness properties at the ends of interval [−1, 1] the rate of weighted approximation by Valleé- Poussin means has the same order as the best weighted approximation of f.

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References

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Authors and Affiliations

  1. Vladikavkaz Scientific Center, Russian Academy of Sciences Daghestan Scientific Center, Russian Academy of Sciences, ul. M. Gadzhieva 45, Makhachkala, 367000, Russia

    I. I. Sharapudinov & M. G. Magomed-Kasumov

Authors
  1. I. I. Sharapudinov
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  2. M. G. Magomed-Kasumov
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Corresponding author

Correspondence to I. I. Sharapudinov.

Additional information

Original Russian Text © I.I. Shapudinov, M.G. Magomed-Kasumov, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 9, pp. 68–80.

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Sharapudinov, I.I., Magomed-Kasumov, M.G. The Valleé-Poussin Means for Special Series With Respect to Ultraspherical Jacobi Polynomials With Sticking Partial Sums. Russ Math. 62, 60–71 (2018). https://doi.org/10.3103/S1066369X18090074

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  • DOI: https://doi.org/10.3103/S1066369X18090074

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