EXTREME VALUES OF FUNCTIONALS AND BEST APPROXIMATION ON CLASSES OF PERIODIC FUNCTIONS

@article{Korneiuk1971EXTREMEVO,
  title={EXTREME VALUES OF FUNCTIONALS AND BEST APPROXIMATION ON CLASSES OF PERIODIC FUNCTIONS},
  author={N. Kornei{\vc}uk},
  journal={Mathematics of The Ussr-izvestiya},
  year={1971},
  volume={5},
  pages={97-129}
}
  • N. Korneičuk
  • Published 1971
  • Mathematics
  • Mathematics of The Ussr-izvestiya
In this paper, we compute upper bounds for the best approximation by trigonometric polynomials in the metrics and on the classes of 2-periodic functions such that , where is a given convex modulus of continuity. In doing this, we obtain a series of results which explain certain new properties of differentiable functions expressed in terms of rearrangements. Also, we obtain precise estimates for functionals of the form , where , and belongs to a certain class of differentiable functions defined… Expand
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On the Best Approximation of Certain Classes of Periodic Functions by Trigonometric Polynomials (pp. 129-144)
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References

On best approximation of continuous functions
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