التفاصيل البيبلوغرافية
| العنوان: |
On Hermite-Hadamard-type inequalities for second order differential inequalities with inverse-square potential |
| المؤلفون: |
Hassen Aydi, Bessem Samet, Manuel De la Sen |
| المصدر: |
AIMS Mathematics, Vol 9, Iss 7, Pp 17955-17970 (2024) |
| بيانات النشر: |
AIMS Press, 2024. |
| سنة النشر: |
2024 |
| المجموعة: |
LCC:Mathematics |
| مصطلحات موضوعية: |
hermite-hadamard-type inequalities, second order differential inequalities, convex functions, convex functions on the coordinates, Mathematics, QA1-939 |
| الوصف: |
We consider the class of functions $ u\in C^2((0, \infty)) $ satisfying second-order differential inequalities in the form $ u''(x)+\frac{k}{x^2}u(x)\geq 0 $ for all $ x > 0 $. For this class of functions, we establish Hermite-Hadamard-type inequalities in both cases ($ k=\frac{1}{4} $ and $ 0 < k < \frac{1}{4} $). We next extend our obtained results to the two-dimensional case. In the limit case $ k\rightarrow 0^+ $ we deriver some existing results from the literature that are related to convex functions and convex functions on the coordinates. In our approach, we make use of some tools from ordinary differential equations. |
| نوع الوثيقة: |
article |
| وصف الملف: |
electronic resource |
| اللغة: |
English |
| تدمد: |
2473-6988 |
| Relation: |
https://doaj.org/toc/2473-6988 |
| DOI: |
10.3934/math.2024874?viewType=HTML |
| DOI: |
10.3934/math.2024874 |
| URL الوصول: |
https://doaj.org/article/10a80e9770534e80af265eaf1237b70e |
| رقم الانضمام: |
edsdoj.10a80e9770534e80af265eaf1237b70e |
| قاعدة البيانات: |
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