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.
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