# Generalized Characteristics of Smoothness and Some Extreme Problems of the Approximation Theory of Functions in the Space *L*_{2}(ℝ)*.* I

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We consider the generalized characteristics of smoothness of the functions ω^{w}(f, t) and Λ^{w}(f, t), t > 0, in the space L_{2}(ℝ) and on the classes \( {L}_2^{\alpha } \) (ℝ) defined with the help of fractional-order derivatives α ϵ (0, ∞) and obtain the exact Jackson-type inequalities for ω^{w}(f).

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