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) |