On best approximations of continuously differentiable functions by splines with respect to two-point rational interpolants
Daghestan Electronic Mathematical Reports, Tome 5 (2016), pp. 49-55.

Voir la notice de l'article provenant de la source Math-Net.Ru

Estimates of degree of the best spline-approximation by means of two-points rational interpolant for continuously differentiable functions on a given segment are obtained.
Keywords: interpolation splines, rational splines, best spline-approximation.
@article{DEMR_2016_5_a4,
     author = {A.-R. K. Ramazanov and V. G. Magomedova},
     title = {On best approximations of continuously differentiable functions by splines with respect to two-point rational interpolants},
     journal = {Daghestan Electronic Mathematical Reports},
     pages = {49--55},
     publisher = {mathdoc},
     volume = {5},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DEMR_2016_5_a4/}
}
TY  - JOUR
AU  - A.-R. K. Ramazanov
AU  - V. G. Magomedova
TI  - On best approximations of continuously differentiable functions by splines with respect to two-point rational interpolants
JO  - Daghestan Electronic Mathematical Reports
PY  - 2016
SP  - 49
EP  - 55
VL  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DEMR_2016_5_a4/
LA  - ru
ID  - DEMR_2016_5_a4
ER  - 
%0 Journal Article
%A A.-R. K. Ramazanov
%A V. G. Magomedova
%T On best approximations of continuously differentiable functions by splines with respect to two-point rational interpolants
%J Daghestan Electronic Mathematical Reports
%D 2016
%P 49-55
%V 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DEMR_2016_5_a4/
%G ru
%F DEMR_2016_5_a4
A.-R. K. Ramazanov; V. G. Magomedova. On best approximations of continuously differentiable functions by splines with respect to two-point rational interpolants. Daghestan Electronic Mathematical Reports, Tome 5 (2016), pp. 49-55. http://geodesic.mathdoc.fr/item/DEMR_2016_5_a4/

[1] Subbotin Yu.N., Chernykh N.I., “Poryadok nailuchshikh splain-priblizhenii nekotorykh klassov funktsii”, Matem. zametki, 7:1 (1970), 31–42 | Zbl

[2] Korneichuk N.P., Splainy v teorii priblizheniya, Nauka, M., 1984 | MR

[3] Subbotin Yu.N., “Variatsii na temu splainov”, Fundament i prikl. matem., 3:4 (1997), 1043–1058 | MR | Zbl

[4] Ramazanov A.-R.K., Magomedova V.G., “Splainy po ratsionalnym interpolyantam”, Dagestanskie Elektronnye Matematicheskie Izvestiya, 4 (2015), 22-31

[5] Lagrange R., “Sur oscillations d`order superior d`une functions numerique”, Ann. sci. Escole norm. super., 82:2 (1965), 101–130, Paris | DOI | MR | Zbl

[6] Sevastyanov E.A., “Kusochno-monotonnaya approksimatsiya i $\Phi$-variatsii”, Analysis Math., 1:2 (1975), 141–164 | DOI | MR | Zbl

[7] Chanturiya Z.A., “O ravnomernoi skhodimosti ryadov Fure”, Matem. sbornik, 100:4 (1976), 534–534 | MR | Zbl

[8] Young L.C., “General inequalities for Stieltjes integrals and the convergence of Fourier series”, Mathem. Ann., 115 (1938), 581–612, London | DOI | MR