On Popoviciu's concept of convexity for functions of $d$ variables
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909587036176384 |
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| author | Komisarski, Andrzej Rajba, Teresa |
| author_facet | Komisarski, Andrzej Rajba, Teresa |
| contents | We establish an integral representation for Popoviciu's convex functions of $d$ variables. This representation serves as a~foundation for deriving several functional inequalities, analogous to those well-known for usual convex functions. Our results generalize and extend the results obtained by S.~Gal, C.~Niculescu, B.~Gavrea, T.~Popoviciu, and others, who considered only differentiable functions of two variables. In contrast to other authors, we do not impose any additional regularity assumptions on the studied functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_13723 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Popoviciu's concept of convexity for functions of $d$ variables Komisarski, Andrzej Rajba, Teresa Classical Analysis and ODEs We establish an integral representation for Popoviciu's convex functions of $d$ variables. This representation serves as a~foundation for deriving several functional inequalities, analogous to those well-known for usual convex functions. Our results generalize and extend the results obtained by S.~Gal, C.~Niculescu, B.~Gavrea, T.~Popoviciu, and others, who considered only differentiable functions of two variables. In contrast to other authors, we do not impose any additional regularity assumptions on the studied functions. |
| title | On Popoviciu's concept of convexity for functions of $d$ variables |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2404.13723 |