Jensen convex functions and doubly stochastic matrices
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909825319829504 |
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| author | Barczy, Matyas Páles, Zsolt |
| author_facet | Barczy, Matyas Páles, Zsolt |
| contents | Given an nxn doubly stochastic matrix P satisfying an appropriate condition of linear algebraic-type, and a function f defined on a nonempty interval, we show that the validity of a convexity-type functional inequality for f in terms P implies that f is Jensen convex. We also prove that if f is convex, then the functional inequality in question holds for all doubly stochastic matrices of any order. The particular case when the doubly stochastic matrix is a circulant one is also considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03715 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Jensen convex functions and doubly stochastic matrices Barczy, Matyas Páles, Zsolt Classical Analysis and ODEs 39B62, 26A51 Given an nxn doubly stochastic matrix P satisfying an appropriate condition of linear algebraic-type, and a function f defined on a nonempty interval, we show that the validity of a convexity-type functional inequality for f in terms P implies that f is Jensen convex. We also prove that if f is convex, then the functional inequality in question holds for all doubly stochastic matrices of any order. The particular case when the doubly stochastic matrix is a circulant one is also considered. |
| title | Jensen convex functions and doubly stochastic matrices |
| topic | Classical Analysis and ODEs 39B62, 26A51 |
| url | https://arxiv.org/abs/2510.03715 |