Iteration groups of functions satisfying a generalized additivity equation
Abstract
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.
References
1. J. Aczél, Gy. Maksa, Equations of generalized bisymmetry and of consistent aggregation: weakly surjective solutions which may be discontinuous at places, J. Math. Anal. Appl. 214 (1997), 22-35.
2. R. Craigen, Zs. Páles, The associativity equation revisited, Aequationes Math. 37 (1989), 306-312.
3. M. Kuczma, An introduction to the theory of functional equations and inequalities, Polish Scientific Publishers & Silesian University, Warszawa-Kraków-Katowice 1985.
4. M. Sablik, Iteration groups of additive functions, European Conference on Iteration Theory, Batschuns, Austria, 10-16 September 1989. World Scientific, Singapore-New Jersey-London-Hong Kong 1991, 305-314.
5. J. Smítal, On a problem of Aczél and Erdős concerning Hamel bases, Aequationes Math. 28 (1985), 135-137.
2. R. Craigen, Zs. Páles, The associativity equation revisited, Aequationes Math. 37 (1989), 306-312.
3. M. Kuczma, An introduction to the theory of functional equations and inequalities, Polish Scientific Publishers & Silesian University, Warszawa-Kraków-Katowice 1985.
4. M. Sablik, Iteration groups of additive functions, European Conference on Iteration Theory, Batschuns, Austria, 10-16 September 1989. World Scientific, Singapore-New Jersey-London-Hong Kong 1991, 305-314.
5. J. Smítal, On a problem of Aczél and Erdős concerning Hamel bases, Aequationes Math. 28 (1985), 135-137.
GerR. (1999). Iteration groups of functions satisfying a generalized additivity equation. Annales Mathematicae Silesianae, 13, 131-141. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14143
Roman Ger
romanger@us.edu.pl
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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