The best asymmetric approximation in spaces of continuous functions

A. V. Pokrovskii

Izvestiya. Mathematics , Tome 70 (2006) no. 4, pp. 809-839.

Résumé

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.

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