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Journal: Annales Mathematicae Silesianae

Iteration groups of functions satisfying a generalized additivity equation

Roman Ger

Language: EN | Published: 30-09-1999 | Abstract | pp. 131-141

An elementary proof of the existence of iteration groups consisting of additive bijections of the real line onto itself and containing nonlinear mappings is presented. An embeddability problem of that kind is also considered. These results are used to get a description of some semigroup automorphisms that are embeddable into an iteration group of automorphisms of the same semigroup.

1999-09-30



Journal: Annales Mathematicae Silesianae

On approximately additive functions

Roman Badora

Language: EN | Published: 30-09-1994 | Abstract | pp. 111-126

In the present paper we find a linear operator on a function space, essentially larger than the space of all bounded functions on an amenable semigroup, which behaves like an invariant mean. This leads to an extension of the Hyers-Ulam stability theorem for Cauchy's functional equation in the case of vector-valued mappings defined on amenable semigroups.

1994-09-30