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 L2(ℝ)
Abstract
The exact values of constants are obtained in the space L2(ℝ) for the Jackson-type inequalities for special moduli of continuity of the k th order defined by the Steklov operator Sh(f) instead of the translation operator Th(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.Downloads
Published
25.06.2014
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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 L2(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.