Ubhaya, Vasant A. \(L_ p\)-approximation from nonconvex subsets of special classes of functions. (English) Zbl 0684.41016 J. Approximation Theory 57, No. 2, 223-238 (1989). 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. Reviewer: N.Nashed Cited in 9 Documents MSC: 41A50 Best approximation, Chebyshev systems Keywords:quasi-convex functions; \(L_ p\)-bounded subsets; super-additive; star- shaped; n-convex functions PDFBibTeX XMLCite \textit{V. A. Ubhaya}, J. Approx. 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