Abstract
Many known results on the iterative equation αi=1 n λiƒi(x) = F(x) require a condition that λ1 > 0 for technical reasons. A problem on the existence of solutions of this iterative equation with the natural restriction λn ≠ 0 is raised. In this paper we study an auxiliary functional equation for its invertible solutions. Then we apply our results on the auxiliary equation to solve the problem in some cases.
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Supported by NSFC Grant, TRAPOYT and China MOE Research Grants
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Zhang, W. On Existence for Polynomial-Like Iterative Equations. Results. Math. 45, 185–194 (2004). https://doi.org/10.1007/BF03323006
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DOI: https://doi.org/10.1007/BF03323006