Some Improvements of the Hermite–Hadamard Integral Inequality
We propose several improvements of the Hermite−Hadamard inequality in the form of linear combination of its end-points and establish best possible constants. Improvements of a second order for the class <inline-formula> <math display="inline"> <semantics> <mr...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/1/117 |
| _version_ | 1817996605802938368 |
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| author | Slavko Simić Bandar Bin-Mohsin |
| author_facet | Slavko Simić Bandar Bin-Mohsin |
| author_sort | Slavko Simić |
| collection | DOAJ |
| description | We propose several improvements of the Hermite−Hadamard inequality in the form of linear combination of its end-points and establish best possible constants. Improvements of a second order for the class <inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="sans-serif">Φ</mi> <mo>(</mo> <mi>I</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> with applications in Analysis and Theory of Means are also given. |
| first_indexed | 2024-04-14T02:24:52Z |
| format | Article |
| id | doaj.art-dddc838580434293ad2cb18ff93a1f41 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-14T02:24:52Z |
| publishDate | 2020-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-dddc838580434293ad2cb18ff93a1f412022-12-22T02:17:56ZengMDPI AGSymmetry2073-89942020-01-0112111710.3390/sym12010117sym12010117Some Improvements of the Hermite–Hadamard Integral InequalitySlavko Simić0Bandar Bin-Mohsin1Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City 758307, VietnamDepartment of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi ArabiaWe propose several improvements of the Hermite−Hadamard inequality in the form of linear combination of its end-points and establish best possible constants. Improvements of a second order for the class <inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="sans-serif">Φ</mi> <mo>(</mo> <mi>I</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> with applications in Analysis and Theory of Means are also given.https://www.mdpi.com/2073-8994/12/1/117convex functionsimpson’s ruledifferentiable function |
| spellingShingle | Slavko Simić Bandar Bin-Mohsin Some Improvements of the Hermite–Hadamard Integral Inequality Symmetry convex function simpson’s rule differentiable function |
| title | Some Improvements of the Hermite–Hadamard Integral Inequality |
| title_full | Some Improvements of the Hermite–Hadamard Integral Inequality |
| title_fullStr | Some Improvements of the Hermite–Hadamard Integral Inequality |
| title_full_unstemmed | Some Improvements of the Hermite–Hadamard Integral Inequality |
| title_short | Some Improvements of the Hermite–Hadamard Integral Inequality |
| title_sort | some improvements of the hermite hadamard integral inequality |
| topic | convex function simpson’s rule differentiable function |
| url | https://www.mdpi.com/2073-8994/12/1/117 |
| work_keys_str_mv | AT slavkosimic someimprovementsofthehermitehadamardintegralinequality AT bandarbinmohsin someimprovementsofthehermitehadamardintegralinequality |