Weighted Hermite–Hadamard integral inequalities for general convex functions
In this article, starting with an equation for weighted integrals, we obtained several extensions of the well-known Hermite–Hadamard inequality. We used generalized weighted integral operators, which contain the Riemann–Liouville and the $ k $-Riemann–Liouville fractional integral operators. The fun...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2023882?viewType=HTML |
| _version_ | 1797529107998703616 |
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| author | Péter Kórus Juan Eduardo Nápoles Valdés Bahtiyar Bayraktar |
| author_facet | Péter Kórus Juan Eduardo Nápoles Valdés Bahtiyar Bayraktar |
| author_sort | Péter Kórus |
| collection | DOAJ |
| description | In this article, starting with an equation for weighted integrals, we obtained several extensions of the well-known Hermite–Hadamard inequality. We used generalized weighted integral operators, which contain the Riemann–Liouville and the $ k $-Riemann–Liouville fractional integral operators. The functions for which the operators were considered satisfy various conditions such as the $ h $-convexity, modified $ h $-convexity and $ s $-convexity. |
| first_indexed | 2024-03-10T10:08:44Z |
| format | Article |
| id | doaj.art-ad28119e6bd84853aca76211bcdc9d32 |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-03-10T10:08:44Z |
| publishDate | 2023-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-ad28119e6bd84853aca76211bcdc9d322023-11-22T01:21:49ZengAIMS PressMathematical Biosciences and Engineering1551-00182023-11-012011199291994010.3934/mbe.2023882Weighted Hermite–Hadamard integral inequalities for general convex functionsPéter Kórus 0Juan Eduardo Nápoles Valdés 1Bahtiyar Bayraktar21. Institute of Applied Pedagogy, Juhász Gyula Faculty of Education, University of Szeged, Hattyas utca 10, H-6725 Szeged, Hungary2. UNNE, FaCENA, Ave. Libertad 5450, Corrientes 3400, Argentina 3. UTN-FRRE, French 414, Resistencia, Chaco 3500, Argentina4. Faculty of Education, Bursa Uludag University, Gorukle Campus, 16059, Bursa, TurkeyIn this article, starting with an equation for weighted integrals, we obtained several extensions of the well-known Hermite–Hadamard inequality. We used generalized weighted integral operators, which contain the Riemann–Liouville and the $ k $-Riemann–Liouville fractional integral operators. The functions for which the operators were considered satisfy various conditions such as the $ h $-convexity, modified $ h $-convexity and $ s $-convexity.https://www.aimspress.com/article/doi/10.3934/mbe.2023882?viewType=HTMLweighted integral operatorsconvex functionsgeneral convex functionshermite–hadamard inequality |
| spellingShingle | Péter Kórus Juan Eduardo Nápoles Valdés Bahtiyar Bayraktar Weighted Hermite–Hadamard integral inequalities for general convex functions Mathematical Biosciences and Engineering weighted integral operators convex functions general convex functions hermite–hadamard inequality |
| title | Weighted Hermite–Hadamard integral inequalities for general convex functions |
| title_full | Weighted Hermite–Hadamard integral inequalities for general convex functions |
| title_fullStr | Weighted Hermite–Hadamard integral inequalities for general convex functions |
| title_full_unstemmed | Weighted Hermite–Hadamard integral inequalities for general convex functions |
| title_short | Weighted Hermite–Hadamard integral inequalities for general convex functions |
| title_sort | weighted hermite hadamard integral inequalities for general convex functions |
| topic | weighted integral operators convex functions general convex functions hermite–hadamard inequality |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2023882?viewType=HTML |
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