Pokrovskii, A. V. 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. Reviewer: Vladimir N. Karpushkin (Moskva) MSC: 41A50 Best approximation, Chebyshev systems 41A52 Uniqueness of best approximation Keywords:approximation; deviation; convex PDF BibTeX XML Cite \textit{A. V. Pokrovskii}, Izv. Math. 70, No. 4, 809--839 (2006; Zbl 1151.41020); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 70, No. 4, 175--208 (2006) Full Text: DOI