Concave shells of continuity modules - Pichugov, S. A. (Ukrains’kyi Matematychnyi Zhurnal, 2019)
UDC 517.9 The inequality$$\overline{ω}(t)≤\inf_{s>0}\left(ω\left(\dfrac{s}{2}\right)+\dfrac{ω(s)}{s}t\right)$$is proved, where $ω(t)$ is a function of the modulus of continuity type and $\overline{ω}(t)$ is its smallest concave majorant. The consequences obtained for Jackson's inequalities in $C_{2π}$ are presented.