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Izv. RAN. Ser. Mat., 2006, Volume 70, Issue 4, Pages 175–208 (Mi izv741)  

The best asymmetric approximation in spaces of continuous functions

A. V. Pokrovskii

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: We consider approximation by convex sets in the space of continuous maps from a compact topological space to a locally convex space with respect to certain asymmetric seminorms. We suggest new criteria for elements of least deviation, make a definition of strongly unique elements of least deviation and study the problems of characterization and existence of such elements. The most detailed study concerns the approximation with a sign-sensitive weight of real-valued continuous functions defined on a compact metric space or on a line segment by elements of the Chebyshev space.

DOI: https://doi.org/10.4213/im741

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English version:
Izvestiya: Mathematics, 2006, 70:4, 809–839

Bibliographic databases:

UDC: 517.518.8
MSC: 41A50, 41A52
Received: 28.07.2005

Citation: A. V. Pokrovskii, “The best asymmetric approximation in spaces of continuous functions”, Izv. RAN. Ser. Mat., 70:4 (2006), 175–208; Izv. Math., 70:4 (2006), 809–839

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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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