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

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In the second part of the paper, we establish the exact Jackson-type inequalities for the characteristic of smoothness Λ^{w} on the classes of functions \( {L}_2^{\alpha}\left(\iota \right) \) defined by the fractional derivatives of order *v 2* (0*,1*) in the space *L*_{2}(ℝ)*.* The exact values of the mean *L*_{2}(*ℝ*) -widths for the classes of functions defined by the generalized characteristics of smoothness ε_{w} and Λ_{w} are also computed.

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