Continuously decreasing solutions for polynomial-like iterative equations |
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| Authors: | Lin Li WenMeng Zhang |
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| Institution: | 14589. College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing, 314001, China
24589. College of Mathematics Science, Chongqing Normal University, Chongqing, 400047, China
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| Abstract: | Most known results on existence, uniqueness and stability for solutions of the polynomial-like iterative equation Σ i=1 n λ i f i (x) = F(x) were obtained in the case of λ 1 ≠ 0. In this paper, we construct C 0 decreasing solutions of the iterative equation in the case that λ 1 can vanish to answer the Leading Coefficient Problem. Moreover, we also give the necessary and sufficiently condition for uniqueness of solutions. |
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