We find the sharp constant in the Jackson-type inequality between the value of the best approximation of functions by trigonometric polynomials and moduli of continuity of m-th order in the spaces Sp, 1 ≤ p < ∞. In the particular case we obtain one result which in a certain sense generalizes the result obtained by L.V. Taykov for m = 1 in the space L2 for the arbitrary moduli of continuity of m-th order (m Є N).
International Journal of Advanced Research in Mathematics (Volume 8)
A. N. Shchitov "On the Jackson-Type Inequality for the Best Sp-Approximations of Functions by Trigonometric Polynomials", International Journal of Advanced Research in Mathematics, Vol. 8, pp. 27-35, 2017