On a Jackson-Type Inequality in the Approximation of a Function by Linear Summation Methods in the Space L_2 - Bozhukha, L. N. (Ukrains’kyi Matematychnyi Zhurnal, 2003)
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.