Jackson-Type Inequalities for the Special Moduli of Continuity on the Entire Real Axis and the Exact Values of Mean ν - Widths for the Classes of Functions in the Space L_2 (ℝ) - Vakarchuk, S. B. (Ukrains’kyi Matematychnyi Zhurnal, 2014)
The exact values of constants are obtained in the space L_2 (ℝ) for the Jackson-type inequalities for special moduli of continuity of the k th order defined by the Steklov operator S_h (f) instead of the translation operator T_h (f) in the case of approximation by entire functions of exponential type σ ∈ (0,∞). The exact values of the mean ν-widths (linear, Bernstein, and Kolmogorov) are also obtained for the classes of functions defined by the indicated characteristic of smoothness.