2019
Том 71
№ 11

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

Bozhukha L. N.

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.

English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 4, pp 648–659.

Citation Example: Bozhukha L. N. On a Jackson-Type Inequality in the Approximation of a Function by Linear Summation Methods in the Space $L_2$ // Ukr. Mat. Zh. - 2003. - 55, № 4. - pp. 537-545.

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