Geodesic
Approximation by cubic splines in the classes of continuously differentiable functions
Matematičeskie zametki, Tome 11 (1972) no. 2, pp. 215-226

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The problem of approximating continuously differentiable periodic functions $f(x)$ by cubic interpolation splines $s_n(f;x)$ with equidistant nodes is considered. Asymptotically exact estimates for $||f(x)-s_n(f;x)||_C$ are obtained in the classes of functions $W^1H_\omega$. 
@article{MZM_1972_11_2_a11,
     author = {V. L. Velikin},
     title = {Approximation by cubic splines in the classes of continuously differentiable functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {215--226},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_11_2_a11/}
}
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V. L. Velikin. Approximation by cubic splines in the classes of continuously differentiable functions. Matematičeskie zametki, Tome 11 (1972) no. 2, pp. 215-226. http://geodesic.mathdoc.fr/item/MZM_1972_11_2_a11/