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The converse problem for a generalized Dhombres functional equation

L. Reich, Jaroslav Smítal, M. Štefánková (2005)

Mathematica Bohemica

We consider the functional equation $f (x f (x)) = ϕ (f (x))$ where $ϕ J \to J$ is a given homeomorphism of an open interval $J \subset (0, \infty)$ and $f (0, \infty) \to J$ is an unknown continuous function. A characterization of the class $𝒮 (J, ϕ)$ of continuous solutions $f$ is given in a series of papers by Kahlig and Smítal 1998–2002, and in a recent paper by Reich et al. 2004, in the case when $ϕ$ is increasing. In the present paper we solve the converse problem, for which continuous maps $f (0, \infty) \to J$ , where $J$ is an interval, there is an increasing homeomorphism $ϕ$ of $J$ such that $f \in 𝒮 (J, ϕ)$ . We...

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Displaying 21 – 40 of 137

The converse problem for a generalized Dhombres functional equation

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Currently displaying 21 – 40 of 137