Ukrainian Mathematical Journal

, Volume 66, Issue 10, pp 1589–1594 | Cite as

On the Third Moduli of Continuity

  • S. I. Bezkryla
  • O. N. Nesterenko
  • A. V. Chaikovs’kyi

An inequality for the third uniform moduli of continuity is proved. This inequality implies that an arbitrary 3-majorant is not necessarily a modulus of continuity of order 3.


Finite Difference Naukova Dumka Satisfying Condition Nonnegative Function Negative Answer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    I. A. Shevchuk, Approximation by Polynomials and Traces of Functions Continuous on the Segment [in Russian], Naukova Dumka, Kiev (1992)Google Scholar
  2. 2.
    S. М. Nikol’skii, “Fourier series with given moduli of continuity,” Dokl. Akad. Nauk USSR, 52, No. 3, 191–194 (1946).Google Scholar
  3. 3.
    S. V. Konyagin, “On the second moduli of continuity,” in: Proc. Steklov Math. Institute, 269 (2010), pp. 1–3.Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • S. I. Bezkryla
    • 1
  • O. N. Nesterenko
    • 1
  • A. V. Chaikovs’kyi
    • 2
  1. 1.National Pedagogical UniversityKyivUkraine
  2. 2.Shevchenko Kyiv National UniversityKyivUkraine

Personalised recommendations