\(L_ p\)-approximation from nonconvex subsets of special classes of functions
The author establishes an existence theorem for a best approximation to a function in \(L_ p\), \(1\leq p\leq \infty\), by functions from a not necessarily convex set under certain general conditions on the set. In addition, properties of \(L_ p\)-bounded subsets are investigated. The unifying development and results are applicable to approximation from subsets of various classes of functions including quasi-convex, convex, super-additive, star-shaped, monotone, and n-convex functions.
scientific article; zbMATH DE number 4120722
scientific article