On well posed generalized best approximation problems
It is proved in the paper, that if \(C\) is both stictly convex and Kadec set in the Banach space \(X\), then the set \(X_{0}(G)\) of all \(x\) in \(X\) such that the problem \(min_{C}(x,G)\) is ill posed is a residual subset of \(X\) provided that \(G\) is closed, bounded relatively weakly compact, nonempty subset of \(X\).
scientific article; zbMATH DE number 1552977