Geodesic
On the modulus of continuity of the operator of best approximation in the space of continuous functions
Matematičeskie zametki, Tome 10 (1971) no. 6, pp. 601-613.

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In the paper we establish estimates for the strong and the weak moduli of continuity of the operator of best approximation in the space of continuous functions. 
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     author = {P. V. Galkin},
     title = {On the modulus of continuity of the operator of best approximation in the space of continuous functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {601--613},
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     volume = {10},
     number = {6},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_6_a1/}
}
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P. V. Galkin. On the modulus of continuity of the operator of best approximation in the space of continuous functions. Matematičeskie zametki, Tome 10 (1971) no. 6, pp. 601-613. http://geodesic.mathdoc.fr/item/MZM_1971_10_6_a1/