# A generalization of the Hahn-Banach theorem

Annales Polonici Mathematici (1993)

- Volume: 58, Issue: 1, page 47-51
- ISSN: 0066-2216

## Access Full Article

top## Abstract

top## How to cite

topJolanta Plewnia. "A generalization of the Hahn-Banach theorem." Annales Polonici Mathematici 58.1 (1993): 47-51. <http://eudml.org/doc/262375>.

@article{JolantaPlewnia1993,

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.},

author = {Jolanta Plewnia},

journal = {Annales Polonici Mathematici},

keywords = {the Hahn-Banach theorem; convex functions; Hahn-Banach theorem; sublinear function},

language = {eng},

number = {1},

pages = {47-51},

title = {A generalization of the Hahn-Banach theorem},

url = {http://eudml.org/doc/262375},

volume = {58},

year = {1993},

}

TY - JOUR

AU - Jolanta Plewnia

TI - A generalization of the Hahn-Banach theorem

JO - Annales Polonici Mathematici

PY - 1993

VL - 58

IS - 1

SP - 47

EP - 51

AB - 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.

LA - eng

KW - the Hahn-Banach theorem; convex functions; Hahn-Banach theorem; sublinear function

UR - http://eudml.org/doc/262375

ER -

## References

top- [1] A. Alexiewicz, Functional Analysis, Monografie Mat. 49, PWN, Warszawa 1969 (in Polish).
- [2] N. Hirano, H. Komiya and W. Takahashi, A generalization of the Hahn-Banach theorem, J. Math. Anal. Appl. 88 (1982), 333-340. Zbl0509.46003
- [3] Z. Kominek, On additive and convex functionals, Rad. Mat. 3 (1987), 267-279. Zbl0643.39006
- [4] H. König, On the abstract Hahn-Banach theorem due to Rodé, Aequationes Math. 34 (1987), 89-95. Zbl0636.46005
- [5] K. Nikodem, On the support of midconvex operators, Aequationes Math. 42 (1991), 182-189. Zbl0747.39006
- [6] G. Rodé, Eine abstrakte Version des Satzes von Hahn-Banach, Arch. Math. (Basel) 31 (1978), 474-481. Zbl0402.46003

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.