TY - JOUR AU - S. A. Pichugov PY - 2019/05/25 Y2 - 2024/03/29 TI - Concave shells of continuity modules JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 71 IS - 5 SE - Short communications DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1470 AB - UDC 517.9 The inequality$$\overline{\omega}(t)\leq\inf_{s>0}\left(\omega\left(\dfrac{s}{2}\right)+\dfrac{\omega(s)}{s}t\right)$$is proved, where $\omega(t)$ 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 $C_{2\pi}$ are presented. ER -