Geodesic
On approximation of multivalued mapping by algebraic polynomial with constraints
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2015), pp. 30-34

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We consider a discrete problem of the best uniform approximation of multivalued mapping by segment images by an algebraic polynomial with constraints upon the value of the approximating polynomial in several nodes of a grid. We establish a criterion of optimality of the solution, which is a generalization of the P. L. Chebyshev's alternance.
Keywords: multivalued mapping, approximating polynomial, alternance optimality conditions. 
@article{IVM_2015_2_a3,
     author = {I. Yu. Vygodchikova},
     title = {On approximation of multivalued mapping by algebraic polynomial with constraints},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {30--34},
     publisher = {mathdoc},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_2_a3/}
}
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I. Yu. Vygodchikova. On approximation of multivalued mapping by algebraic polynomial with constraints. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2015), pp. 30-34. http://geodesic.mathdoc.fr/item/IVM_2015_2_a3/