Abstract
The work is devoted to the solution of a number of extremal problems of approximation theory of functions on the real axis \( \mathbb{R} \). In the space L 2(\( \mathbb{R} \)), the exact constants in Jackson-type inequalities are calculated. The exact values of average ν-widths are obtained for the classes of functions from L 2(\( \mathbb{R} \)) that are defined by averaged k-order moduli of continuity and for the classes of functions defined by K-functionals. In the chronological order, the sufficiently complete analysis of the final results related to the solution of extremal problems of approximation theory in the periodic case and on the whole real axis is carried out.
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