Geodesic
One-Sided Approximation of Truncated Powers by Algebraic Polynomials in the Mean
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 185-193.

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Estimates for one-sided approximation of truncated powers by algebraic polynomials in the space $L_1$ are obtained. 
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V. P. Motornyi; O. V. Motornaya. One-Sided Approximation of Truncated Powers by Algebraic Polynomials in the Mean. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 185-193. http://geodesic.mathdoc.fr/item/TM_2005_248_a17/

[1] Nikolskii S.M., “O nailuchshem priblizhenii mnogochlenami v srednem funktsii $|a-x|^s$”, Izv. AN SSSR. Ser. mat., 11:2 (1947), 139–180 | MR | Zbl

[2] Nikolskii S.M., “O nailuchshem lineinom metode priblizheniya mnogochlenami v srednem differentsiruemykh funktsii”, DAN SSSR, 58:2 (1947), 185–188 | MR | Zbl

[3] Ganelius T., “On one-sided approximation by trigonometrical polynomials”, Math. scand., 4 (1956), 247–258 | MR | Zbl

[4] Doronin V.G., Ligun A.A., “Tochnye znacheniya verkhnikh granei nailuchshikh priblizhenii klassov v metrike $L_1$”, Issledovaniya po sovremennym problemam summirovaniya i priblizheniya funktsii i ikh prilozheniyam, Dnepropetr. un-t, Dnepropetrovsk, 1977, 25–36 | MR

[5] Doronin V.G., Ligun A.A., “O nailuchshem odnostoronnem priblizhenii klassov $W^rH_\omega$”, Mat. zametki, 21:3 (1977), 313–327 | MR | Zbl

[6] Korneichuk N.P., Ligun A.A., Doronin V.G., Approksimatsiya s ogranicheniyami, Nauk. dumka, Kiev, 1982, 250 pp. | MR

[7] Motornyi V.P., Pas'ko A.N., “On the best one-sided approximation of some classes of differentiable functions in $L_1$”, East. J. Approx., 10:1–2 (2004), 159–169 | MR | Zbl

[8] Motornyi V.P., Pasko A.N., “Nailuchshee odnostoronnee priblizhenie usechennykh stepenei i otsenki pogreshnosti kvadraturnykh formul na nekotorykh klassakh funktsii”, Vestn. Dnepropetr. un-ta. Matematika, 2003, no. 8, 74–80

[9] Babenko V.F., Kofanov V.A., “Nesimmetrichnye priblizheniya klassov differentsiruemykh funktsii algebraicheskimi mnogochlenami v srednem”, Anal. Math., 14:3 (1988), 193–217 | DOI | MR | Zbl

[10] Motornaya O.V., O nailuchshem priblizhenii differentsiruemykh funktsii algebraicheskimi mnogochlenami v prostranstve $L_1$, Preprint 93-20, Inst. matematiki AN Ukrainy, Kiev, 1993, 30 pp. | MR

[11] Turetskii A.Kh., Teoriya interpolirovaniya v zadachakh, Vysh. shk., Minsk, 1977, 256 pp. | MR | Zbl

[12] Motornyi V.P., Motornaya O.V., Pasko A.N., “Priblizhenie differentsiruemykh funktsii interpolyatsionnymi polinomami s kratnymi uzlami v srednem”, Vestn. Dnepropetr. un-ta. Matematika, 2004, no. 9, 65–72