ArticleOriginal scientific text
Title
A generalization of the Hahn-Banach theorem
Authors 1
Affiliations
- Institute of Mathematics, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland
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.
Keywords
the Hahn-Banach theorem, convex functions
Bibliography
- A. Alexiewicz, Functional Analysis, Monografie Mat. 49, PWN, Warszawa 1969 (in Polish).
- N. Hirano, H. Komiya and W. Takahashi, A generalization of the Hahn-Banach theorem, J. Math. Anal. Appl. 88 (1982), 333-340.
- Z. Kominek, On additive and convex functionals, Rad. Mat. 3 (1987), 267-279.
- H. König, On the abstract Hahn-Banach theorem due to Rodé, Aequationes Math. 34 (1987), 89-95.
- K. Nikodem, On the support of midconvex operators, Aequationes Math. 42 (1991), 182-189.
- G. Rodé, Eine abstrakte Version des Satzes von Hahn-Banach, Arch. Math. (Basel) 31 (1978), 474-481.
Pages:
47-51
Main language of publication
English
Received
1991-11-16
Accepted
1992-05-20
Published
1993
Exact and natural sciences