Functions Commuting With an Arbitrary Fixed Bijection

Authors

  • Andrzej Mach Faculty of Engineering and Economics, The State Higher School of Vocational Education, Ciechanów, Poland

DOI:

https://doi.org/10.5644/SJM.09.2.07

Keywords:

Bijective function, commuting function, iteration, closed and open orbits, Babbage functional equation

Abstract

In this note a characterization of all bijective functions commuting with a fixed bijection $\varphi:X \to X$, where $X$ is an arbitrary nonempty set, is given.

 

2010 Mathematics Subject Classification. Primary 39B12; Secondary 26A18

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References

D. Krassowska and M. C. Zdun, On limit sets of mixed iterates of commuting mappings, Aequationes Math., 78 (2009), 283–295.

D. Krassowska and M. C. Zdun, On the embeddability of commuting continuous injections in iteration semigroups, Publicationes Math., 75 (2009), 179–190.

D. Krassowska, Iteration groups and commuting functions in ${R}^n$, Grazer Math. Berichte, 351 (2007), 100–109.

M. Kuczma, Functional Equations in a Single Variable, Monografie Mat. 46, Polish Scientific Publishers (PWN), Warszawa 1968.

A. Mach, The translation equation on certain n-groups, Aequationes Math., 47 (1994), 11–30.

A. Mach, The construction of the solutions of the generalized translation equation, Aequationes Math., 64 (2002), 1–23.

A. Mach, On some functional equations involving Babbage equation, Result. Math., 51 (2007), 97–106

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Published

07.06.2024

How to Cite

Mach, A. (2024). Functions Commuting With an Arbitrary Fixed Bijection. Sarajevo Journal of Mathematics, 9(2), 221–230. https://doi.org/10.5644/SJM.09.2.07

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Articles