# 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)

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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.

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Entire Function Approximation Theory Exponential Type Function Sinc Require Equality
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