An analog of the Jackson–Chernykh inequality for spline approximations in the space L2( ℝ) is established in this work. For r ℕ and σ > 0, we denote by Aσr( f )2 the best approximation of a function f ∈ L2(ℝ ) by the space of splines of degree r of minimal defect with knots , j ∏/σ , and by ω( f, δ)2 the first-order modulus of continuity of f in L2( ℝ). The main result of our work is as follows. For any f ∈ L2( ℝ),(formula presented) where θr = 1/√1-εr 2 and εr is the positive root of the equation(formula presented) The constant 1/√2 cannot be reduced on the whole class L2(ℝ ) even by increasing the step of the modulus of continuity.
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