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Mathematical Notes

, Volume 92, Issue 3–4, pp 458–472 | Cite as

Jackson-Stechkin type inequalities for special moduli of continuity and widths of function classes in the space L 2

  • S. B. VakarchukEmail author
  • V. I. Zabutnaya
Article

Abstract

We obtain sharp Jackson-Stechkin type inequalities for moduli of continuity of kth order Ω k in which, instead of the shift operator T h f, the Steklov operator S h (f) is used. Similar smoothness characteristic of functions were studied earlier in papers of Abilov, Abilova, Kokilashvili, and others. For classes of functions defined by these characteristics, we calculate the exact values of certain n-widths.

Keywords

Jackson-Stechkin type inequality modulus of continuity Steklov operator Sh(f) n-width Fourier series Minkowski’s inequality 

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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Dnepropetrovsk University of Economics and LawDnepropetrovskUkraine

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