Displaying similar documents to “Uniform convexity of Köthe-Bochner function spaces.”

A generalization of the Hahn-Banach theorem

Jolanta Plewnia (1993)

Annales Polonici Mathematici

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If C is a non-empty convex subset of a real linear space E, p: E → ℝ is a sublinear function and f:C → ℝ is concave and such that f ≤ p on C, then there exists a linear function g:E → ℝ such that g ≤ p on E and f ≤ g on C. In this result of Hirano, Komiya and Takahashi we replace the sublinearity of p by convexity.

Remarks on some properties in the geometric theory of Banach spaces

Wagdy Gomaa El-Sayed, Krzysztof Fraczek (1996)

Commentationes Mathematicae Universitatis Carolinae

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The aim of this paper is to derive some relationships between the concepts of the property of strong ( α ' ) introduced recently by Hong-Kun Xu and the so-called characteristic of near convexity defined by Goebel and Sȩkowski. Particularly we provide very simple proof of a result obtained by Hong-Kun Xu.