Displaying similar documents to “Fréchet's equation and Hyers theorem on noncommutative semigroups”

On separation theorems for subadditive and superadditive functionals

Zbigniew Gajda, Zygfryd Kominek (1991)

Studia Mathematica

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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...

Perturbations of bi-continuous semigroups

Bálint Farkas (2004)

Studia Mathematica

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The notion of bi-continuous semigroups has recently been introduced to handle semigroups on Banach spaces that are only strongly continuous for a topology coarser than the norm-topology. In this paper, as a continuation of the systematic treatment of such semigroups started in [20-22], we provide a bounded perturbation theorem, which turns out to be quite general in view of various examples.