Commuting functions and simultaneous Abel equations

• Autorzy: W. Jarczyk , K. Łoskot , M. C. Zdun
• Języki publikacji: EN

Abstrakty

EN

The system of Abel equations
α(f_t(x)) = α(x) + λ(t), t ∈ T,
is studied under the general assumption that $f_t$ are pairwise commuting homeomorphisms of a real interval and have no fixed points (T is an arbitrary non-empty set). A result concerning embeddability of rational iteration groups in continuous groups is proved as a simple consequence of the obtained theorems.

Słowa kluczowe

EN

Abel equation; commuting functions; iteration group

Kategorie tematyczne

• 26A18: Iteration
• 39B12: Iteration theory, iterative and composite equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1994-1995
• Tom: 60
• Numer: 2
• Strony: 119-135

Daty

wydano

1994

otrzymano

1992-12-15

Twórcy

autor

W. Jarczyk

• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

autor

K. Łoskot

• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

autor

M. C. Zdun

• Institute of Mathematics, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland

Bibliografia

• [1] J. Dugundji and A. Granas, Fixed Point Theory, Vol. 1, Monografie Mat. 61, Polish Scientific Publishers, Warszawa, 1982.
• [2] W. Jarczyk, A recurrent method of solving iterative functional equations, Prace Naukowe Uniw. Śląsk. Katowic. 1206, Katowice, 1991.
• [3] M. Kuczma, Functional Equations in a Single Variable, Monografie Mat. 46, Polish Scientific Publishers, Warszawa, 1968.
• [4] M. C. Zdun, Note on commutable functions, Aequationes Math. 36 (1988), 153-164.
• [5] M. C. Zdun, On simultaneous Abel equations, Aequationes Math. 38 (1989), 163-177.
• [6] M. C. Zdun, On the orbits of disjoint groups of continuous functions, Rad. Mat., to appear.
• [7] M. C. Zdun, Some remarks on the iterates of commuting functions, in: European Conference on Iteration Theory, Lisbon, 1991, J. P. Lampreia et al. (eds.), World Scientific, Singapore, 1992, 336-342.