A generalization of the Hahn-Banach theorem
Volume 58 / 1993
Annales Polonici Mathematici 58 (1993), 47-51
DOI: 10.4064/ap-58-1-47-51
Abstract
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.
