A new generalization of some quantum integral inequalities for quantum differentiable convex functions
Abstract In this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequ...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-04-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-021-03382-0 |
| _version_ | 1818600458283909120 |
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| author | Yi-Xia Li Muhammad Aamir Ali Hüseyin Budak Mujahid Abbas Yu-Ming Chu |
| author_facet | Yi-Xia Li Muhammad Aamir Ali Hüseyin Budak Mujahid Abbas Yu-Ming Chu |
| author_sort | Yi-Xia Li |
| collection | DOAJ |
| description | Abstract In this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint–trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results. |
| first_indexed | 2024-12-16T12:35:48Z |
| format | Article |
| id | doaj.art-22661536dc65472387eabc6ee697a2f8 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-16T12:35:48Z |
| publishDate | 2021-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-22661536dc65472387eabc6ee697a2f82022-12-21T22:31:34ZengSpringerOpenAdvances in Difference Equations1687-18472021-04-012021111510.1186/s13662-021-03382-0A new generalization of some quantum integral inequalities for quantum differentiable convex functionsYi-Xia Li0Muhammad Aamir Ali1Hüseyin Budak2Mujahid Abbas3Yu-Ming Chu4College of Mathematics and Finance, Xiangnan UniversityJiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal UniversityDepartment of Mathematics, Faculty of Science and Arts, Düzce UniversityDepartment of Mathematics, Government College UniversityDepartment of Mathematics, Huzhou UniversityAbstract In this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint–trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.https://doi.org/10.1186/s13662-021-03382-0Hermite–Hadamard inequalityTrapezoid inequalitiesMidpoint inequalitiesQuantum calculusConvex functions |
| spellingShingle | Yi-Xia Li Muhammad Aamir Ali Hüseyin Budak Mujahid Abbas Yu-Ming Chu A new generalization of some quantum integral inequalities for quantum differentiable convex functions Advances in Difference Equations Hermite–Hadamard inequality Trapezoid inequalities Midpoint inequalities Quantum calculus Convex functions |
| title | A new generalization of some quantum integral inequalities for quantum differentiable convex functions |
| title_full | A new generalization of some quantum integral inequalities for quantum differentiable convex functions |
| title_fullStr | A new generalization of some quantum integral inequalities for quantum differentiable convex functions |
| title_full_unstemmed | A new generalization of some quantum integral inequalities for quantum differentiable convex functions |
| title_short | A new generalization of some quantum integral inequalities for quantum differentiable convex functions |
| title_sort | new generalization of some quantum integral inequalities for quantum differentiable convex functions |
| topic | Hermite–Hadamard inequality Trapezoid inequalities Midpoint inequalities Quantum calculus Convex functions |
| url | https://doi.org/10.1186/s13662-021-03382-0 |
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