Cauchy--Schwarz-type inequalities for additive functions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913233684660224 |
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| author | Páles, Zsolt Shihab, Mahmood Kamil |
| author_facet | Páles, Zsolt Shihab, Mahmood Kamil |
| contents | The main goal of this paper is to show that if a real valued function defined on a groupoid satisfies a certain Levi--Civita-type functional equation, then it also fulfills a Cauchy--Schwarz-type functional inequality. In particular, if the groupoid is the multiplicative structure of commutative ring, then we can establish the existence of nontrivial additive functions satisfying inequalities connected to the multiplicative structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08587 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cauchy--Schwarz-type inequalities for additive functions Páles, Zsolt Shihab, Mahmood Kamil Rings and Algebras The main goal of this paper is to show that if a real valued function defined on a groupoid satisfies a certain Levi--Civita-type functional equation, then it also fulfills a Cauchy--Schwarz-type functional inequality. In particular, if the groupoid is the multiplicative structure of commutative ring, then we can establish the existence of nontrivial additive functions satisfying inequalities connected to the multiplicative structure. |
| title | Cauchy--Schwarz-type inequalities for additive functions |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2402.08587 |