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)

Authors

  • S. B. Vakarchuk Днепропетр. ун-т им. А. Нобеля

Abstract

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.

Published

25.06.2014

Issue

Section

Research articles

How to Cite

Vakarchuk, S. B. “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)”. Ukrains’kyi Matematychnyi Zhurnal, vol. 66, no. 6, June 2014, pp. 740–766, https://umj.imath.kiev.ua/index.php/umj/article/view/2175.