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.
@article{bwmeta1.element.bwnjournal-article-apmv58z1p47bwm,
author = {Jolanta Plewnia},
title = {A generalization of the Hahn-Banach theorem},
journal = {Annales Polonici Mathematici},
volume = {58},
year = {1993},
pages = {47-51},
zbl = {0805.46003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv58z1p47bwm}
}
Jolanta Plewnia. A generalization of the Hahn-Banach theorem. Annales Polonici Mathematici, Tome 58 (1993) pp. 47-51. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv58z1p47bwm/
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