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Solarity of sets in max-approximation problems. (English) Zbl 1442.41010
The author discusses the solarity and stability of the max-projection operator for a class of max-approximation problems. Some solarity and stability properties are derived by the Brouwer fixed point theorem and the Park fixed point theorem. Moreover, in view of the stability of the max-projection operator, some conditions to ensure a set to be a local max-sun are given.
MSC:
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
47H10 Fixed-point theorems
52A30 Variants of convex sets (star-shaped, (\(m, n\))-convex, etc.)
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