On generalized Dhombres equations with nonconstant polynomial solutions in the complex plane |
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| Authors: | Ludwig Reich Jaroslav Smítal |
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| Institution: | 1. Institut für Mathematik, Karl-Franzens Universit?t Graz, 8010, Graz, Austria
2. Mathematical Institute, Silesian University, 746 01, Opava, Czech Republic
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| Abstract: | We characterize functional equations of the form ${f(zf(z))=f(z)^{k+1},z\in\mathbb {C}}$ , with ${k\in\mathbb N}$ , like those generalized Dhombres equations ${f(zf(z))=\varphi (f(z))}$ , ${z\in\mathbb C}$ , with given entire function ${\varphi}$ , which have a nonconstant polynomial solution f. |
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