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arXiv · 2604.14244

Higher regularity of solutions of an iterative functional equation

Liang Feng·Xiao Tang
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Abstract

In this paper, we investigate the existence of $C^n$, $n\in \mathbb{N}^+$, solutions for a class of second-order iterative functional equations involving iterates of the unknown function and a nonlinear term. Applying the Fiber Contraction Theorem and Fa\`a di Bruno's Formula, we establish the existence of bounded $C^n$ solutions with bounded derivatives of order from $1$ to $n$.

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Liang Feng, Xiao Tang. 2026-04-15. Higher regularity of solutions of an iterative functional equation. https://arxiv.org/abs/2604.14244

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