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On the stability of the translation equation. (English) Zbl 1212.26009
The author investigates the stability of the translation equation $$F(t,F(s,x))=F(s+t,x)$$, where $$F:(0,\infty)\times I\to I$$ is continuous and $$I$$ is a real interval. The stability of the translation equation in some classes of functions, or in the ring of formal power series has been studied by A. Mach and Z. Moszner [Aequationes Math. 72, No. 1–2, 191–197 (2006; Zbl 1104.39024)] and W. Jablońsky and L. Reich [Sitzungsber., Abt. II, Österr. Akad. Wiss., Math.-Naturwiss. Kl. 215, 127–137 (2006; Zbl 1159.39316)], respectively.

MSC:
 26A18 Iteration of real functions in one variable 39B12 Iteration theory, iterative and composite equations