Geodesic
Rational approximation of continuous functions of finite variation
Izvestiya. Mathematics , Tome 9 (1975) no. 5, pp. 1081-1118.

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In this paper, a bound is established for the least uniform deviation of rational functions from a continuous function of bounded variation with a given modulus of continuity. It is shown that the bound obtained is sharp. Bibliography: 8 titles. 
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A. P. Bulanov. Rational approximation of continuous functions of finite variation. Izvestiya. Mathematics , Tome 9 (1975) no. 5, pp. 1081-1118. http://geodesic.mathdoc.fr/item/IM2_1975_9_5_a7/

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[2] Bulanov A. P., “Asimptotika dlya naimenshikh uklonenii funktsii $\operatorname{sign}x$ ot ratsionalnykh funktsii”, Matem. sb., 96(138):2 (1975), 171–188 | MR | Zbl

[3] Dolzhenko E. P., “Ob osobykh tochkakh nepreryvnykh garmonicheskikh funktsii”, Izv. AN SSSR. Ser. matem., 28:6 (1964), 1251–1270 | MR | Zbl

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

[7] Dolzhenko E. P., “Sravnenie skorostei ratsionalnoi i polinomialnoi approksimatsii”, Matem. zametki, 1:3 (1967), 313–320 | Zbl

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