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The best asymmetric approximation in spaces of continuous functions. (English. Russian original) Zbl 1151.41020
Izv. Math. 70, No. 4, 809-839 (2006); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 70, No. 4, 175-208 (2006).
The paper represents the most abstract branch of approximation theory. It is concerned with the approximation by elements of convex sets in the space of continuous maps from a compact topological space to a locally convex space with respect to certain asymmetric seminorms. A new criterion for elements of least deviationis proposed, see N. G. Chebotarev [A minimax criterion and its applications, Collected papers, Vol. 2, Akad. Nauk SSSR, Moskow-Leningrad 396–409 (1949)]. The problem of existence of such elements and their characterization is studied.
MSC:
41A50 Best approximation, Chebyshev systems
41A52 Uniqueness of best approximation
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