Geodesic
Approximation of double-valued function by an algebraic polynomial
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2016), pp. 8-13

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We consider the minimax model of nonlinear structure for approximation of double-valued function by an algebraic polynomial. We give the conditions of optimality in the form of far-reaching generalization of P. L. Chebyshev's alternance conditions in the problem of approximation of a function by a polynomial.
Keywords: minimax, nonsmooth analysis, double-valued function, selector, approximating polynomial. 
@article{IVM_2016_4_a1,
     author = {I. Yu. Vygodchikova},
     title = {Approximation of double-valued function by an algebraic polynomial},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {8--13},
     publisher = {mathdoc},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_4_a1/}
}
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I. Yu. Vygodchikova. Approximation of double-valued function by an algebraic polynomial. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2016), pp. 8-13. http://geodesic.mathdoc.fr/item/IVM_2016_4_a1/