Geodesic
Rational approximations to convex functions with given modulus of con­tinuity
Sbornik. Mathematics, Tome 13 (1971) no. 3, pp. 473-490 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that for any convex continuous functions $f(x)$ ($x\in[a,b]$, $-\infty) with modulus of continuity $\omega(\delta)$ the order of approximation by rational functions does not exceed $$ C\cdot\frac{\ln^2n}n\cdot\inf_{0<\lambda<1}\biggl\{\omega(\lambda)+M\cdot\frac{\ln^2n}n\cdot\ln\frac{b-a}\lambda\biggr\}, $$ where $C$ is an absolute constant and $M=\max|f(x)|$. Bibliography: 6 titles. 
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     title = {Rational approximations to convex functions with given modulus of con\-tinuity},
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A. P. Bulanov. Rational approximations to convex functions with given modulus of con­tinuity. Sbornik. Mathematics, Tome 13 (1971) no. 3, pp. 473-490. http://geodesic.mathdoc.fr/item/SM_1971_13_3_a8/

[1] A. P. Bulanov, “O poryadke priblizheniya vypuklykh funktsii ratsionalnymi funktsiyami”, Izv. AN SSSR, seriya matem., 33 (1969), 1132–1148 | MR | Zbl

[2] P. Szusz, P. Turan, “On the constractive theory of function”, Magyar Tud. Acad. Mat. Kutato Int. Kozl., 1 (1965), 495–502 | MR

[3] A. P. Bulanov, “O nailuchshikh ratsionalnykh priblizheniyakh vypuklykh funktsiyu i funktsii s konechnym izmeneniem”, DAN SSSR, 190:1 (1970), 13–14 | MR | Zbl

[4] A. .A. Gonchar, “O skorosti ratsionalnoi approksimatsii nepreryvnykh funktsii s kharakternymi osobennostyami”, Matem. sb., 73(115) (1967), 630–638 | MR | Zbl

[5] I. P. Natanson, Konstruktivnaya teoriya funktsii, Gostekhizdat, Moskva, 1949

[6] S. A. Telyakovskii, “Dve teoremy o priblizhenii funktsii algebraicheskimi mnogochlenami”, Matem. sb., 70(112) (1966), 252–265