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

Abstract

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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.

How to cite

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Nikodem, 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

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

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