Ukrainian Mathematical Journal

, Volume 71, Issue 5, pp 819–824 | Cite as

Concave Shells of Continuity Modules

  • S. A. PichugovEmail author
We prove the inequality
$$ \overline{\omega}(t)\le \underset{s>0}{\operatorname{inf}}\left(\omega \left(\frac{s}{2}\right)+\frac{\omega (s)}{s}t\right), $$

where ω(t) is a function of the modulus-of-continuity type and \( \overline{\omega}(t) \) is its smallest concave majorant.

The consequences obtained for Jackson’s inequalities in Care presented.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dnepr National University of Railway TransportDneprUkraine

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