On a Jackson-Type Inequality in the Approximation of a Function by Linear Summation Methods in the Space L 2

We prove a statement on exact inequalities between the deviations of functions from their linear methods (in the metric of L₂) with multipliers defined by a continuous function and majorants determined as the scalar product of the squared modulus of continuity (of order r) in L₂ for the lth derivative of the function and a certain weight function . We obtain several corollaries of the general theorem.