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ArticleOriginal scientific text

Title

On separation theorems for subadditive and superadditive functionals

Authors 1, 1

Affiliations

  1. Department of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

Abstract

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.

Bibliography

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Studia Mathematica
1991/100/1
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Pages:
25-38
Main language of publication
English
Received
1990-05-10
Accepted
1990-07-20
Published
1991
Exact and natural sciences