Higher regularity of solutions of an iterative functional equation
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913036563906560 |
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| author | Feng, Liang Tang, Xiao |
| author_facet | Feng, Liang Tang, Xiao |
| contents | 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 Faà di Bruno's Formula, we establish the existence of bounded $C^n$ solutions with bounded derivatives of order from $1$ to $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14244 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Higher regularity of solutions of an iterative functional equation Feng, Liang Tang, Xiao General Mathematics 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 Faà di Bruno's Formula, we establish the existence of bounded $C^n$ solutions with bounded derivatives of order from $1$ to $n$. |
| title | Higher regularity of solutions of an iterative functional equation |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2604.14244 |