A generalization of the Hahn-Banach theorem

• Autorzy: Jolanta Plewnia
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

the Hahn-Banach theorem; convex functions

Kategorie tematyczne

• 46A22: Theorems of Hahn-Banach type; extension and lifting of functionals and operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1993
• Tom: 58
• Numer: 1
• Strony: 47-51

Daty

wydano

1993

otrzymano

1991-11-16

poprawiono

1992-05-20

poprawiono

1992-07-16

Twórcy

autor

Jolanta Plewnia

• Institute of Mathematics, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland

Bibliografia

• [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.
• [3] Z. Kominek, On additive and convex functionals, Rad. Mat. 3 (1987), 267-279.
• [4] H. König, On the abstract Hahn-Banach theorem due to Rodé, Aequationes Math. 34 (1987), 89-95.
• [5] K. Nikodem, On the support of midconvex operators, Aequationes Math. 42 (1991), 182-189.
• [6] G. Rodé, Eine abstrakte Version des Satzes von Hahn-Banach, Arch. Math. (Basel) 31 (1978), 474-481.