Commuting functions and simultaneous Abel equations

W. Jarczyk; K. Łoskot; M. Zdun

ArticleOriginal scientific text

Title

Commuting functions and simultaneous Abel equations

Authors ¹, ¹, ²

Affiliations

Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
Institute of Mathematics, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland

Abstract

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.

Keywords

ENG

Abel equation, commuting functions, iteration group

J. Dugundji and A. Granas, Fixed Point Theory, Vol. 1, Monografie Mat. 61, Polish Scientific Publishers, Warszawa, 1982.
W. Jarczyk, A recurrent method of solving iterative functional equations, Prace Naukowe Uniw. Śląsk. Katowic. 1206, Katowice, 1991.
M. Kuczma, Functional Equations in a Single Variable, Monografie Mat. 46, Polish Scientific Publishers, Warszawa, 1968.
M. C. Zdun, Note on commutable functions, Aequationes Math. 36 (1988), 153-164.
M. C. Zdun, On simultaneous Abel equations, Aequationes Math. 38 (1989), 163-177.
M. C. Zdun, On the orbits of disjoint groups of continuous functions, Rad. Mat., to appear.
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.

Title

Commuting functions and simultaneous Abel equations

Affiliations

Abstract

Keywords

Bibliography