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iterative functional equation; invariant curves; monotone solutions

References:

[1] J. Dhombres: **Applications associatives ou commutatives**. C. R. Acad. Sci. Paris 281 (1975), 809–812. MR 0419662 | Zbl 0344.39009

[2] P. Kahlig, J. Smítal: **On the solutions of a functional equation of Dhombres**. Results Math. 27 (1995), 362–367. DOI 10.1007/BF03322840 | MR 1331109

[3] P. Kahlig, J. Smítal: **On a parametric functional equation of Dhombres type**. Aequationes Math. 56 (1998), 63–68. DOI 10.1007/s000100050044 | MR 1628303

[4] P. Kahlig, J. Smítal: **On a generalized Dhombres functional equation**. Aequationes Math. 62 (2001), 18–29. DOI 10.1007/PL00000138 | MR 1849137

[5] M. Kuczma: **Functional Equations in a Single Variable**. Polish Scientific Publishers, Warsaw, 1968. MR 0228862 | Zbl 0196.16403

[6] M. Kuczma, B. Choczewski, R. Ger: **Iterative Functional Equations**. Encyclopedia of Mathematics and its Applications Vol. 32, Cambridge University Press, Cambridge, 1990. MR 1067720