# Abstract separation theorems of Rodé type and their applications

Kazimierz Nikodem; Zsolt Páles; Szymon Wąsowicz

Annales Polonici Mathematici (1999)

- Volume: 72, Issue: 3, page 207-217
- ISSN: 0066-2216

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topNikodem, Kazimierz, Páles, Zsolt, and Wąsowicz, Szymon. "Abstract separation theorems of Rodé type and their applications." Annales Polonici Mathematici 72.3 (1999): 207-217. <http://eudml.org/doc/262715>.

@article{Nikodem1999,

abstract = {Sufficient and necessary conditions are presented under which two given functions can be separated by a function Π-affine in Rodé sense (resp. Π-convex, Π-concave). As special cases several old and new separation theorems are obtained.},

author = {Nikodem, Kazimierz, Páles, Zsolt, Wąsowicz, Szymon},

journal = {Annales Polonici Mathematici},

keywords = {convex (midconvex), affine (Jensen) function; Rodé's theorem, separation theorem; subadditive, additive, sublinear, linear function; separation theorems; Hahn-Banach theorem; additive; subadditive; midpoint-convex; generalized affine functions; inequalities},

language = {eng},

number = {3},

pages = {207-217},

title = {Abstract separation theorems of Rodé type and their applications},

url = {http://eudml.org/doc/262715},

volume = {72},

year = {1999},

}

TY - JOUR

AU - Nikodem, Kazimierz

AU - Páles, Zsolt

AU - Wąsowicz, Szymon

TI - Abstract separation theorems of Rodé type and their applications

JO - Annales Polonici Mathematici

PY - 1999

VL - 72

IS - 3

SP - 207

EP - 217

AB - Sufficient and necessary conditions are presented under which two given functions can be separated by a function Π-affine in Rodé sense (resp. Π-convex, Π-concave). As special cases several old and new separation theorems are obtained.

LA - eng

KW - convex (midconvex), affine (Jensen) function; Rodé's theorem, separation theorem; subadditive, additive, sublinear, linear function; separation theorems; Hahn-Banach theorem; additive; subadditive; midpoint-convex; generalized affine functions; inequalities

UR - http://eudml.org/doc/262715

ER -

## References

top- [1] K. Baron, J. Matkowski and K. Nikodem, A sandwich with convexity, Math. Pannonica 5 (1994), 139-144. Zbl0803.39011
- [2] E. Behrends and K. Nikodem, A selection theorem of Helly type and its applications, Studia Math. 116 (1995), 43-48. Zbl0847.52004
- [3] B G. Buskes, The Hahn-Banach Theorem surveyed, Dissert. Math. 327 (1993). Zbl0808.46003
- [4] B. Fuchssteiner and W. Lusky, Convex Cones, North-Holland Math. Stud. 56, North-Holland, Amsterdam, 1981. Zbl0478.46002
- [5] N. Hirano, H. Komiya and W. Takahashi, A generalization of the Hahn-Banach theorem, J. Math. Anal. Appl. 88 (1982), 333-340. Zbl0509.46003
- [6] K R. Kaufman, Interpolation of additive functionals, Studia Math. 27 (1966), 269-272. Zbl0143.36302
- [7] H. König, On the abstract Hahn-Banach Theorem due to Rodé, Aequationes Math. 34 (1987), 89-95. Zbl0636.46005
- [8] P. Kranz, Additive functionals on abelian semigroups, Comment. Math. Prace Mat. 16 (1972), 239-246. Zbl0262.20087
- [9] S. Mazur et W. Orlicz, Sur les espaces métriques linéaires II, Studia Math. 13 (1953), 137-179.
- [10] K. Nikodem, E. Sadowska and S. Wąsowicz, A note on separation by subadditive and sublinear functions, Ann. Mat. Sil., to appear. Zbl0978.39020
- [11] K. Nikodem and S. Wąsowicz, A sandwich theorem and Hyers-Ulam stability of affine functions, Aequationes Math. 49 (1995), 160-164. Zbl0815.39010
- [12] Z. Páles, Geometric versions of Rodé's theorem, Rad. Mat. 8 (1992), 217-229. Zbl0937.46005
- [13] R G. Rodé, Eine abstrakte Version des Satzes von Hahn-Banach, Arch. Math. (Basel) 31 (1978), 474-481. Zbl0402.46003
- [14] P. Volkmann and H. Weigel, Systeme von Funktionalgleichungen, ibid. 37 (1981), 443-449. Zbl0458.39004

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