Geodesic
Best approximations of continuous functions by spline functions
Matematičeskie zametki, Tome 8 (1970) no. 1, pp. 41-46.

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An investigation of the approximation on $[0, 1]$ of functions $f(x)$ by spline functions $s(f,\varphi;x)$ of degree $2r-1$ and of deficiency $r$ ($r>1$) depending on the vector function $\varphi=\{\varphi_1(x),\dots,\varphi_{r-1}(x)\}$ and interpolating $f(x)$ at fixed points. For the optimal choice of the vector $\varphi_0$, exact estimates are obtained of the norms $||f(x)-s(f,\varphi_0;x)||_{C[0,1]}$ and $||f(x)-s(f,\varphi_0;x)||_{L[0,1]}$ on the function classes $H_\omega$. 
@article{MZM_1970_8_1_a4,
     author = {V. L. Velikin},
     title = {Best approximations of continuous functions by spline functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {41--46},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_1_a4/}
}
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V. L. Velikin. Best approximations of continuous functions by spline functions. Matematičeskie zametki, Tome 8 (1970) no. 1, pp. 41-46. http://geodesic.mathdoc.fr/item/MZM_1970_8_1_a4/