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Exact bounds for the uniform approximation of continuous periodic functions by r-th order splines

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Abstract

We solve the problem of determining exact bounds for the uniform approximation of continuous periodic functions by r-th order interpolation splines in a space C and on a class Hω specified by the convex modulus of continuityω(t).

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Authors and Affiliations

  1. Dnepropetrovsk State University, USSR

    A. A. Zhensykbaev

Authors
  1. A. A. Zhensykbaev
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Translated from Matematicheskie Zametki, Vol. 13, No. 2, pp. 217–228, February, 1972.

In conclusion the author wishes to express his deep gratitude to N. P. Korneichuka for constant attention and observations which were useful to him in preparing the paper.

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Zhensykbaev, A.A. Exact bounds for the uniform approximation of continuous periodic functions by r-th order splines. Mathematical Notes of the Academy of Sciences of the USSR 13, 130–136 (1973). https://doi.org/10.1007/BF01094230

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  • DOI: https://doi.org/10.1007/BF01094230

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