A note on Jackson's theorem for differentiable functions

From previously published results of the author on the exact upper bound of best approximations by trigonometric polynomials for classes of periodic differentiable functions are derived the values of the exact constants in Jackson's inequalities for $2\pi$-periodic functions $f\in C^r$ with modulus of continuity $\omega(f^{(r)}; t)$ for the $r$-th derivative which is convex upwards.