A functional inequality and its relation to convexity of vector-valued functions
| Autor: | Hsu, Ih Ching |
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| Zdroj: | Proceedings of the American Mathematical Society; 1976, Vol. 58 Issue: 1 p119-123, 5p |
| Abstrakt: | With respect to a partial ordering $ \ll $ $ F(s) + tG(s) \ll F(s + t)$ is strongly convex and has a Riemann type integral representation, even a Bochner type integral representation when the functional inequality is considered in a Banach lattice. The paper also proves the equivalence of strong and weak convexity in an ordered locally convex space whose positive cone is closed. As an application, an affirmative answer is given to an open question raised earlier by R. G. Kuller and the author. |
| Databáze: | Supplemental Index |
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