Geodesic
Linear approximation method preserving $k$-monotonicity
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 21-27

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The paper presents the example of linear finite-dimensional approximation method that preserves $k$-monotonicity of approximated functions and uses the values of function at equidistant points on $[0,1]$.
Keywords: shape-preserving approximation, linear approximation, degree of approximation. 
@article{SEMR_2015_12_a66,
     author = {D. I. Boytsov and S. P. Sidorov},
     title = {Linear approximation method preserving $k$-monotonicity},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {21--27},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a66/}
}
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D. I. Boytsov; S. P. Sidorov. Linear approximation method preserving $k$-monotonicity. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 21-27. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a66/