W-approximative compactness and continuity of the generalized projection operator in Banach spaces

• Autores: Bo Guan, Wen Song
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 162, Nº 1, 2010, págs. 64-71
• Idioma: inglés
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• Resumen

  • We introduce the notion of W-approximative (weak) compactness for a nonempty subset of a smooth Banach space, and present its characterizations. With this notion, we give the sufficient conditions for continuity and the upper semi-continuity of the generalized projection operator.