Recent results on functional equations in a single variable, perspectives and open problems

By K. Baron. 2001

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Characteristic solutions of polynomial-like iterative equations (2004, background): “Recently many mathematicians in the fields of functional equations and dynamical systems were concerned with iterative equations (see, e.g., [ 1 , 2, 5, 6, 10, 15, 17, 18]), where iterates of unknown functions are involved.”
Iterative functional equations (2009, background): “Let y be a strictly monotonous continuous function R 7→ I ⊂ R and y[−1] its inverse I 7→ R, then the functions f [n](x) = y ( n+ y[−1](x) ) (1.1) with integer n are the n-th iterates of the strictly increasing function f = f [1] : I 7→ I. Classical books concerning iterates are Aczél [1] and Kuczma ”