A convexity-type functional inequality with infinite convex combinations
Given a function f defined on a nonempty and convex subset of the d-dimensional Euclidean space, we prove that if f is bounded from below and it satisfies a convexity-type functional inequality with infinite convex combinations, then f has to be convex. We also give alternative proofs of a generaliz...
Elmentve itt :
| Szerzők: | |
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2025
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| Sorozat: | ANNALES UNIVERSITATIS SCIENTIARUM BUDAPESTINENSIS DE ROLANDO EOTVOS NOMINATAE SECTIO COMPUTATORICA
58 |
| Tárgyszavak: | |
| doi: | 10.71352/ac.58.040825 |
| mtmt: | 36297367 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/38039 |
| Tartalmi kivonat: | Given a function f defined on a nonempty and convex subset of the d-dimensional Euclidean space, we prove that if f is bounded from below and it satisfies a convexity-type functional inequality with infinite convex combinations, then f has to be convex. We also give alternative proofs of a generalization of some known results on convexity with infinite convex combinations due to Daróczy and Páles (1987) and Pavić (2019) using a probabilistic version of Jensen inequality. |
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| Terjedelem/Fizikai jellemzők: | 47-55 |
| ISSN: | 0138-9491 |