A Note on The Convexity of Chebyshev Sets



Título del documento: A Note on The Convexity of Chebyshev Sets
Revista: Boletim da Sociedade Paranaense de Matematica
Base de datos: PERIÓDICA
Número de sistema: 000394631
ISSN: 0037-8712
Autores: 1
2
Instituciones: 1Guru Nanak Dev University, Department of Mathematics, Amritsar. India
2Amardeep Singh Shergill Memorial College, Department of Mathematics, Mukandpur. India
Año:
Volumen: 27
Número: 1
Paginación: 59-63
País: Brasil
Idioma: Inglés
Tipo de documento: Artículo
Enfoque: Analítico
Resumen en inglés 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
Disciplinas: Matemáticas
Palabras clave: 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
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