On <i>q</i>-Hermite-Hadamard Inequalities for Differentiable Convex Functions
In this paper, we establish some new results on the left-hand side of the <i>q</i>-Hermite−Hadamard inequality for differentiable convex functions with a critical point. Our work extends the results of Alp et. al (<i>q</i>-Hermite Hadamard inequalities and quantum e...
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| Format: | Article |
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MDPI AG
2019-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/7/632 |
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| author | Seksan Jhanthanam Jessada Tariboon Sotiris K. Ntouyas Kamsing Nonlaopon |
| author_facet | Seksan Jhanthanam Jessada Tariboon Sotiris K. Ntouyas Kamsing Nonlaopon |
| author_sort | Seksan Jhanthanam |
| collection | DOAJ |
| description | In this paper, we establish some new results on the left-hand side of the <i>q</i>-Hermite−Hadamard inequality for differentiable convex functions with a critical point. Our work extends the results of Alp et. al (<i>q</i>-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions, J. King Saud Univ. Sci., 2018, 30, 193-203), by considering the critical point-type inequalities. |
| first_indexed | 2024-12-22T04:54:22Z |
| format | Article |
| id | doaj.art-e14b79fdba144390b711bb8efd2354cc |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-22T04:54:22Z |
| publishDate | 2019-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e14b79fdba144390b711bb8efd2354cc2022-12-21T18:38:24ZengMDPI AGMathematics2227-73902019-07-017763210.3390/math7070632math7070632On <i>q</i>-Hermite-Hadamard Inequalities for Differentiable Convex FunctionsSeksan Jhanthanam0Jessada Tariboon1Sotiris K. Ntouyas2Kamsing Nonlaopon3Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandDepartment of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, ThailandDepartment of Mathematics, University of Ioannina, 45110 Ioannina, GreeceDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandIn this paper, we establish some new results on the left-hand side of the <i>q</i>-Hermite−Hadamard inequality for differentiable convex functions with a critical point. Our work extends the results of Alp et. al (<i>q</i>-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions, J. King Saud Univ. Sci., 2018, 30, 193-203), by considering the critical point-type inequalities.https://www.mdpi.com/2227-7390/7/7/632Hermite-Hadamard inequalities<i>q</i>-derivative<i>q</i>-integralconvex functions |
| spellingShingle | Seksan Jhanthanam Jessada Tariboon Sotiris K. Ntouyas Kamsing Nonlaopon On <i>q</i>-Hermite-Hadamard Inequalities for Differentiable Convex Functions Mathematics Hermite-Hadamard inequalities <i>q</i>-derivative <i>q</i>-integral convex functions |
| title | On <i>q</i>-Hermite-Hadamard Inequalities for Differentiable Convex Functions |
| title_full | On <i>q</i>-Hermite-Hadamard Inequalities for Differentiable Convex Functions |
| title_fullStr | On <i>q</i>-Hermite-Hadamard Inequalities for Differentiable Convex Functions |
| title_full_unstemmed | On <i>q</i>-Hermite-Hadamard Inequalities for Differentiable Convex Functions |
| title_short | On <i>q</i>-Hermite-Hadamard Inequalities for Differentiable Convex Functions |
| title_sort | on i q i hermite hadamard inequalities for differentiable convex functions |
| topic | Hermite-Hadamard inequalities <i>q</i>-derivative <i>q</i>-integral convex functions |
| url | https://www.mdpi.com/2227-7390/7/7/632 |
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