
Journal of Convex Analysis 19 (2012), No. 4, 11531166 Copyright Heldermann Verlag 2012 Best Approximation Problems in Compactly Uniformly Rotund Spaces Julian P. Revalski Inst. of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Street  Block 8, 1113 Sofia, Bulgaria revalski@math.bas.bg Nikolay V. Zhivkov Inst. of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Street  Block 8, 1113 Sofia, Bulgaria niz@abv.bg We investigate under what geometric conditions the best approximation problem to a nonempty closed subset of a real Banach space is generalized wellposed, or, more generally, the problem either has no solution or is generalized wellposed, for the majority of the points in the space. "Majority" is understood as a set whose complement in the space is σporous or σcone supported. Analogously to the case when uniqueness of the best approximation is considered, it turns out that certain local uniform, or uniform, properties of the norm of the underlying space have to be required. Keywords: Best approximation, metric projection, wellposedness, approximative compactness, Baire category, porous sets, cone supported sets, compact uniform rotundity. MSC: 41A65, 46B20 [ Fulltextpdf (154 KB)] for subscribers only. 