Concave shells of continuity modules

  • S. A. Pichugov Днепропетр. нац. ун-т ж.-д. трансп.

Abstract

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.
Published
25.05.2019
How to Cite
PichugovS. A. “Concave Shells of Continuity Modules”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, no. 5, May 2019, pp. 716-20, http://umj.imath.kiev.ua/index.php/umj/article/view/1470.
Section
Short communications