A generalization of the Hahn-Banach theorem

Jolanta Plewnia

Annales Polonici Mathematici (1993)

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

Abstract

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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.

How to cite

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Jolanta 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

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

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