On the exact constant in Jackson-Stechkin inequality for the uniform metric

摘要

The classical Jackson-Stechkin inequality estimates the value of the bestuniform approximation of a periodic function by trigonometric polynomials ofdegree $\le n-1$ in terms of its $r$-th modulus of smoothness$\omega_r(f,\delta)$. The main result of the paper is in establishing the correct order ofJackson--Stechkin constants.