In the space
L 2 of real-valued measurable 2
π-periodic functions that are square summable on the period 0, 2
π], the Jackson-Stechkin inequality
$$E_n (f) \leqslant \mathcal{K}_n (\delta ,\omega )\omega (\delta ,f), f \in L^2 $$
, is considered, where
E n (
f) is the value of the best approximation of the function
f by trigonometric polynomials of order at most
n and
ω(
δ,
f) is the modulus of continuity of the function
f in
L 2 of order 1 or 2. The value
$$\mathcal{K}_n (\delta ,\omega ) = \sup \left\{ {\frac{{E_n (f)}}{{\omega (\delta ,f)}}:f \in L^2 } \right\}$$
is found at the points
δ = 2
π/m (where
m ∈ ?) for
m ≥ 3
n 2 + 2 and
ω =
ω 1 as well as for
m ≥ 11
n 4/3 ? 1 and
ω =
ω 2.