Ukrainian Mathematical Journal

, Volume 68, Issue 12, pp 1920–1928 | Cite as

Some Properties of the Moduli of Continuity of Periodic Functions in Metric Spaces

  • S. A. Pichugov
Let L 0(T) be the set of real-valued periodic measurable functions, let Ψ: R + → R + be the modulus of continuity, and let
$$ {L}_{\Psi}\equiv {L}_{\Psi}(T)=\left\{f\in {L}_0(T):{\left\Vert f\right\Vert}_{\Psi}\coloneq \frac{1}{2\uppi}\underset{T}{\int}\Psi \left(\left|f(x)\right|\right) dx<\infty \right\}. $$

We study the properties of multiple moduli of continuity for the functions from L Ψ.


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • S. A. Pichugov
    • 1
  1. 1.Dnepropetrovsk National University of Railway TransportDnepropetrovskUkraine

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