On Hermite-Hadamard-type inequalities for systems of partial differential inequalities in the plane
We establish necessary conditions for the existence of solutions to various systems of partial differential inequalities in the plane. The obtained conditions provide new Hermite-Hadamard-type inequalities for differentiable functions in the plane. In particular, we obtain a refinement of an inequal...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2023-09-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2023-0115 |
| Summary: | We establish necessary conditions for the existence of solutions to various systems of partial differential inequalities in the plane. The obtained conditions provide new Hermite-Hadamard-type inequalities for differentiable functions in the plane. In particular, we obtain a refinement of an inequality due to Dragomir [On the Hadamard’s inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwan. J. Math. 5 (2001), no. 4, 775–788] for convex functions on the coordinates. |
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| ISSN: | 2391-5455 |