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1991 | 100 | 1 | 25-38
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On separation theorems for subadditive and superadditive functionals

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Języki publikacji
EN
Abstrakty
EN
We generalize the well known separation theorems for subadditive and superadditive functionals to some classes of not necessarily Abelian semigroups. We also consider the problem of supporting subadditive functionals by additive ones in the not necessarily commutative case. Our results are motivated by similar extensions of the Hyers stability theorem for the Cauchy functional equation. In this context the so-called weakly commutative and amenable semigroups appear naturally. The relations between these two classes of semigroups are discussed at the end of the paper.
Słowa kluczowe
Czasopismo
Rocznik
Tom
100
Numer
1
Strony
25-38
Opis fizyczny
Daty
wydano
1991
otrzymano
1990-05-10
poprawiono
1990-07-20
poprawiono
1990-10-23
Twórcy
  • Department of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
  • Department of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
Bibliografia
  • [1] A. Chaljub-Simon und P. Volkmann, Bemerkungen zu einem Satz von Rodé, manuscript.
  • [2] M. M. Day, Amenable semigroups, Illinois J. Math. 1 (1957), 509-544.
  • [3] G. L. Forti, Remark 11, Report of Meeting, the 22nd Internat Symposium on Functional Equations, Aequationes Math. 29 (1985), 90-91.
  • [4] G. L. Forti, The stability of homomorphisms and amenability with applications to functional equations, Università degli Studi di Milano, Quaderno 24, 1986.
  • [5] Z. Gajda, Invariant means and representations of semigroups in the theory of functional equations, submitted.
  • [6] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. I, Springer, Berlin 1963.
  • [7] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224.
  • [8] R. Kaufman, Interpolation of additive functionals, Studia Math. 27 (1966), 269-272.
  • [9] H. König, On the abstract Hahn-Banach theorem due to Rodé, Aequationes Math. 34 (1987), 89-95.
  • [10] P. Kranz, Additive functionals on abelian semigroups, Prace Mat. (Comment. Math.) 16 (1972), 239-246.
  • [11] J. Rätz, On approximately additive mappings, in: General Inequalities 2, Internat. Ser. Numer. Math. 47, Birkhäuser, Basel 1980, 233-251.
  • [12] G. Rodé, Eine abstrakte Version des Satzes von Hahn-Banach, Arch. Math. (Basel) 31 (1978), 474-481.
  • [13] L. Székelyhidi, Remark 17, Report of Meeting, the 22nd Internat. Symposium on Functional Equations, Aequationes Math. 29 (1985), 95-96.
  • [14] J. Tabor, Remark 18, ibid., 96.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv100i1p25bwm
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