Geodesic
On the best approximation in the mean of continuous functions by polynomials, which are majorized by a given function
Matematičeskie zametki, Tome 11 (1972) no. 4, pp. 365-374 Cet article a éte moissonné depuis la source Math-Net.Ru

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We discuss the problem of the best approximation in the mean of functions, which are continuous on a segment, by the polynomials in a differentiable Chebyshev system that do not exceed a given differentiable function. We prove that the extremal polynomial is unique and develop its characteristic properties. 
@article{MZM_1972_11_4_a1,
     author = {V. A. Kaminskii},
     title = {On the best approximation in the mean of continuous functions by polynomials, which are majorized by a given function},
     journal = {Matemati\v{c}eskie zametki},
     pages = {365--374},
     year = {1972},
     volume = {11},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_11_4_a1/}
}
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V. A. Kaminskii. On the best approximation in the mean of continuous functions by polynomials, which are majorized by a given function. Matematičeskie zametki, Tome 11 (1972) no. 4, pp. 365-374. http://geodesic.mathdoc.fr/item/MZM_1972_11_4_a1/