Geodesic
Accurate estimates of deviations of spline approximations to classes of differentiable functions
Matematičeskie zametki, Tome 9 (1971) no. 5, pp. 483-494.

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We derive the approximation on $[0,1]$ of functions $f(x)$ by interpolating spline-functions $s_r(f;x)$ of degree $2r+1$ and defect $r+1$ ($r=1,2,\dots$). Exact estimates for $|f(x)-s_r(f;x)|$ and $\|f(x)-s_r(f;x)\|_C$ on the class $W^mH_\omega$ for $m=1$, $r=1,2,\dots$ and $m=2,3$, $r=2$ for the case of convex $\omega(t)$, are derived. 
@article{MZM_1971_9_5_a1,
     author = {V. L. Velikin and N. P. Korneichuk},
     title = {Accurate estimates of deviations of spline approximations to classes of differentiable functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {483--494},
     publisher = {mathdoc},
     volume = {9},
     number = {5},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_9_5_a1/}
}
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V. L. Velikin; N. P. Korneichuk. Accurate estimates of deviations of spline approximations to classes of differentiable functions. Matematičeskie zametki, Tome 9 (1971) no. 5, pp. 483-494. http://geodesic.mathdoc.fr/item/MZM_1971_9_5_a1/