Improved regularity for a composite functional equation stemming from the theory of means
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910024665661440 |
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| author | Kiss, Tibor Tóth, Péter |
| author_facet | Kiss, Tibor Tóth, Péter |
| contents | In this paper we describe the solutions of the functional equation \begin{equation*} F\Big(\frac{x+y}2\Big)+f_1(x)+f_2(y)=G \big(g_1(x)+g_2(y)) \end{equation*} defined on an open subinterval of $ \mathbb{R} $. Improving previous results we assume differentiability on each involved function, eliminate a former condition on $ g'_1 $ and $ g'_2$, moreover we determine a brand new family of solutions. We also present a particular member of this class as an example. In order to achieve this, we strengthen known results about certain auxiliary functional equations as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15541 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Improved regularity for a composite functional equation stemming from the theory of means Kiss, Tibor Tóth, Péter Classical Analysis and ODEs In this paper we describe the solutions of the functional equation \begin{equation*} F\Big(\frac{x+y}2\Big)+f_1(x)+f_2(y)=G \big(g_1(x)+g_2(y)) \end{equation*} defined on an open subinterval of $ \mathbb{R} $. Improving previous results we assume differentiability on each involved function, eliminate a former condition on $ g'_1 $ and $ g'_2$, moreover we determine a brand new family of solutions. We also present a particular member of this class as an example. In order to achieve this, we strengthen known results about certain auxiliary functional equations as well. |
| title | Improved regularity for a composite functional equation stemming from the theory of means |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2602.15541 |