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| Format: | Preprint |
| Publié: |
2026
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2604.26704 |
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| _version_ | 1866917482820796416 |
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| author | Kiss, Tibor |
| author_facet | Kiss, Tibor |
| contents | Here, we investigate the solutions to equation \[f(f(-x)+x)=f(-f(x))+f(x),\qquad x\in\mathbb{R}\] that are prescribed on the non-positive half-line. We will refer to this prescribed function as the generator of the corresponding solution.
We show that any function taking negative values on the negative half-line and being strictly greater than the identity can be extended to a solution. Nevertheless, the solutions generated by continuous, strictly monotone functions can be well characterized. As our main result, we establish a closed-form expression for these functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26704 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quasi graph-additive functions with a prescribed branch Kiss, Tibor Classical Analysis and ODEs Here, we investigate the solutions to equation \[f(f(-x)+x)=f(-f(x))+f(x),\qquad x\in\mathbb{R}\] that are prescribed on the non-positive half-line. We will refer to this prescribed function as the generator of the corresponding solution. We show that any function taking negative values on the negative half-line and being strictly greater than the identity can be extended to a solution. Nevertheless, the solutions generated by continuous, strictly monotone functions can be well characterized. As our main result, we establish a closed-form expression for these functions. |
| title | Quasi graph-additive functions with a prescribed branch |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2604.26704 |