Geodesic
A note on Jackson's theorem for differentiable functions
Matematičeskie zametki, Tome 12 (1972) no. 5, pp. 517-522.

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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. 
@article{MZM_1972_12_5_a2,
     author = {N. P. Korneichuk},
     title = {A note on {Jackson's} theorem for differentiable functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {517--522},
     publisher = {mathdoc},
     volume = {12},
     number = {5},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_5_a2/}
}
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N. P. Korneichuk. A note on Jackson's theorem for differentiable functions. Matematičeskie zametki, Tome 12 (1972) no. 5, pp. 517-522. http://geodesic.mathdoc.fr/item/MZM_1972_12_5_a2/