Geodesic
Inequalities of type generalized Jackson theorem for best approximations
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 27, Tome 404 (2012), pp. 135-156

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Very simple methods to get upper estimates of type generalized Jackson theorem for best approximations of periodic function are proposed. These results are similar to generalized Jackson theorem which gives estimates in terms of moduli of continuity. 
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     author = {V. V. Zhuk},
     title = {Inequalities of type generalized {Jackson} theorem for best approximations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {135--156},
     publisher = {mathdoc},
     volume = {404},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_404_a7/}
}
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V. V. Zhuk. Inequalities of type generalized Jackson theorem for best approximations. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 27, Tome 404 (2012), pp. 135-156. http://geodesic.mathdoc.fr/item/ZNSL_2012_404_a7/