# On a Jackson-Type Inequality in the Approximation of a Function by Linear Summation Methods in the Space $L_2$

### Abstract

We prove a statement on exact inequalities between the deviations of functions from their linear methods (in the metric of $L_2$) with multipliers defined by a continuous function and majorants determined as the scalar product of the squared modulus of continuity (of order r) in $L_2$ for the lth derivative of the function and a certain weight function θ. We obtain several corollaries of the general theorem.
Published

25.04.2003

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 55, no. 4, Apr. 2003, pp. 537-45, https://umj.imath.kiev.ua/index.php/umj/article/view/3927.

Issue

Section

Short communications