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

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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.

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  1. Dneprodzerzhinsk Technical University, Dneprodzerzhinsk

    L. N. Bozhukha

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  1. L. N. Bozhukha
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Bozhukha, L.N. On a Jackson-Type Inequality in the Approximation of a Function by Linear Summation Methods in the Space L 2 . Ukrainian Mathematical Journal 55, 648–659 (2003). https://doi.org/10.1023/B:UKMA.0000010164.14145.4c

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  • DOI: https://doi.org/10.1023/B:UKMA.0000010164.14145.4c

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