Geodesic
Best approximations of continuous functions by piecewise monotone functions
Izvestiya. Mathematics, Tome 8 (1974) no. 5, pp. 991-1008 
A. S. Loginov. Best approximations of continuous functions by piecewise monotone functions. Izvestiya. Mathematics, Tome 8 (1974) no. 5, pp. 991-1008. http://geodesic.mathdoc.fr/item/IM2_1974_8_5_a2/
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     author = {A. S. Loginov},
     title = {Best approximations of continuous functions by piecewise monotone functions},
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     volume = {8},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1974_8_5_a2/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In the present article we establish the characteristic theorem of best approximation of a continuous function by piecewise monotone functions. Starting from this theorem we find a sharp estimate for the best approximation.

[1] Malozemov V. N., “Ob otklonenii lomanykh”, Vestn. LGU, 1966, no. 7, 150–153 | MR | Zbl

[2] Loginov A. S., “Priblizhenie nepreryvnykh funktsii lomanymi”, Matem. zametki, 6:2 (1969), 149–160 | MR | Zbl

[3] Loginov A. S., “Otsenki priblizheniya lomanymi nepreryvnykh funktsii klassa $H_\omega$”, Vestn. MGU, seriya I, matem., mekhanika, 1970, no. 6, 47–55 | MR | Zbl

[4] Velikin V. L., “O nailuchshem priblizhenii splain-funktsiyami na klassakh nepreryvnykh funktsii”, Matem. zametki, 8:1 (1970), 41–46 | MR | Zbl

[5] Loginov A. S., “Ob odnom predelnom sootnoshenii priblizheniya splain-funktsiyami”, Ukr. matem. zh., 24:5 (1972), 695–700 | MR

[6] Rice J. R., “Characterization of Chebyshev approximation by splines”, SIAM J. Numer. Anal., 4:4 (1967), 557–565 | DOI | MR | Zbl

[7] Natanson I. P., Konstruktivnaya teoriya funktsii, GITTL, M., L., 1949