Geodesic
On polynomials of the best approximation in the Hausdorff metric
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 22, Tome 217 (1994), pp. 130-143 
A. P. Petukhov. On polynomials of the best approximation in the Hausdorff metric. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 22, Tome 217 (1994), pp. 130-143. http://geodesic.mathdoc.fr/item/ZNSL_1994_217_a10/
@article{ZNSL_1994_217_a10,
     author = {A. P. Petukhov},
     title = {On polynomials of the best approximation in the {Hausdorff} metric},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {130--143},
     year = {1994},
     volume = {217},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_217_a10/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A definition of the Hausdorff alternance is given. In these terms we obtain a sufficient condition for an algebraic polynomial to have minimal deviation from the function $f$ in the Hausdorff $\alpha$-metric. A condition under which a polynomial $P_n$ is the unique polynomial of best approximation to a function $f$, as well as a necessary condition for $P_n$ to have minimal deviation from $f$ are established. Also, similar theorems for $2\pi$-periodic functions are stated. Bibliography: 3 titles.