Open Access
2009 Conjugacy of P-configurations and nonlinear solutions to a certain conditional Cauchy equation
Orr Moshe Shalit
Banach J. Math. Anal. 3(1): 28-35 (2009). DOI: 10.15352/bjma/1240336420
Abstract

We study the connection between conjugations of a special kind of dynamical systems, called P-configurations, and solutions to homogeneous Cauchy type functional equations. We find that any two regular P-configurations are conjugate by a homeomorphism, but cannot be conjugate by a diffeomorphism. This leads us to the following conclusion (answering an open question posed by Paneah): there exist continuous nonlinear solutions to the functional equation: $$ f(t) = f\left(\frac{t+1}{2}\right) + f\left(\frac{t-1}{2}\right) \,\, , \,\, t \in [-1,1] . $$

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Copyright © 2009 Tusi Mathematical Research Group
Orr Moshe Shalit "Conjugacy of P-configurations and nonlinear solutions to a certain conditional Cauchy equation," Banach Journal of Mathematical Analysis 3(1), 28-35, (2009). https://doi.org/10.15352/bjma/1240336420
Published: 2009
Vol.3 • No. 1 • 2009
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