Error estimates and Lipschitz constants for best approximation in continuous function spaces

✍ Scribed by M. Bartelt; W. Li

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 771 KB
• Volume: 30
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/0898-1221(95)00104-2

✦ Synopsis

We use a structural characterization of the metric projection PG(f), from the continuous function space to its one-dimensional subspace G, to derive a lower bound of the Hausdorff strong unicity constant (or weak sharp minimum constant) for PG and then show this lower bound can be attained. Then the exact value of Lipschitz constant for PG is computed. The process is a quantitative analysis based on the G~teaux derivative of PG, a representation of local Lipschitz constants, the equivalence of local and global Lipschitz constants for lower semicontinuous mappings, and construction of functions. geywords--Error bounds, Lipschitz constants, G£teaux derivatives, Metric projections, Strong uniqueness.