| Journal: | Boletim da Sociedade Paranaense de Matematica |
| Database: | PERIÓDICA |
| System number: | 000394631 |
| ISSN: | 0037-8712 |
| Authors: | Narang, T.D1 Sangeeta2 |
| Institutions: | 1Guru Nanak Dev University, Department of Mathematics, Amritsar. India 2Amardeep Singh Shergill Memorial College, Department of Mathematics, Mukandpur. India |
| Year: | 2009 |
| Volumen: | 27 |
| Number: | 1 |
| Pages: | 59-63 |
| Country: | Brasil |
| Language: | Inglés |
| Document type: | Artículo |
| Approach: | Analítico |
| English abstract | Perhaps one of the major unsolved problem in Approximation Theory is : Whether or not every Chebyshev subset of a Hilbert space must be convex. Many partial answers to this problem are available in the literature. R.R. Phelps [Proc. Amer. Math. Soc. 8 (1957), 790-797] showed that a Chebyshev set in an inner product space (or in a strictly convex normed linear space) is convex if the associated metric projection is non-expansive. We extend this result to metric spaces |
| Disciplines: | Matemáticas |
| Keyword: | Matemáticas puras, Conjuntos convexos, Conjuntos de Chebyshev, Teoría de la aproximación, Espacios de Hilbert, Espacios métricos |
| Keyword: | Mathematics, Pure mathematics, Convex sets, Chebyshev sets, Approximation theory, Hilbert spaces, Metric spaces |
| Full text: | Texto completo (Ver PDF) |
