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

The classical Jackson-Stechkin inequality estimates the value of the best uniform approximation of a periodic function by trigonometric polynomials of degree $\le n-1$ 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 of Jackson--Stechkin constants.