Some new integral inequalities for higher-order strongly exponentially convex functions
Abstract Integral inequalities with generalized convexity play an important role in both applied and theoretical mathematics. The theory of integral inequalities is currently one of the most rapidly developing areas of mathematics due to its wide range of applications. In this paper, we study the co...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-03-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-023-02952-y |
| _version_ | 1797859809902460928 |
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| author | Jaya Bisht Nidhi Sharma Shashi Kant Mishra Abdelouahed Hamdi |
| author_facet | Jaya Bisht Nidhi Sharma Shashi Kant Mishra Abdelouahed Hamdi |
| author_sort | Jaya Bisht |
| collection | DOAJ |
| description | Abstract Integral inequalities with generalized convexity play an important role in both applied and theoretical mathematics. The theory of integral inequalities is currently one of the most rapidly developing areas of mathematics due to its wide range of applications. In this paper, we study the concept of higher-order strongly exponentially convex functions and establish a new Hermite–Hadamard inequality for the class of strongly exponentially convex functions of higher order. Further, we derive some new integral inequalities for Riemann–Liouville fractional integrals via higher-order strongly exponentially convex functions. These findings include several well-known results and newly obtained results as special cases. We believe that the results presented in this paper are novel and will be beneficial in encouraging future research in this field. |
| first_indexed | 2024-04-09T21:35:36Z |
| format | Article |
| id | doaj.art-3a6cca4e6c6a4fe38714ca1c8f4c2a83 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-09T21:35:36Z |
| publishDate | 2023-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-3a6cca4e6c6a4fe38714ca1c8f4c2a832023-03-26T11:19:31ZengSpringerOpenJournal of Inequalities and Applications1029-242X2023-03-012023111910.1186/s13660-023-02952-ySome new integral inequalities for higher-order strongly exponentially convex functionsJaya Bisht0Nidhi Sharma1Shashi Kant Mishra2Abdelouahed Hamdi3Department of Mathematics, Institute of Science, Banaras Hindu UniversityDepartment of Mathematics, Institute of Science, Banaras Hindu UniversityDepartment of Mathematics, Institute of Science, Banaras Hindu UniversityMathematics Program, Department of Mathematics, Statistics and Physics, College of Arts and Sciences, Qatar UniversityAbstract Integral inequalities with generalized convexity play an important role in both applied and theoretical mathematics. The theory of integral inequalities is currently one of the most rapidly developing areas of mathematics due to its wide range of applications. In this paper, we study the concept of higher-order strongly exponentially convex functions and establish a new Hermite–Hadamard inequality for the class of strongly exponentially convex functions of higher order. Further, we derive some new integral inequalities for Riemann–Liouville fractional integrals via higher-order strongly exponentially convex functions. These findings include several well-known results and newly obtained results as special cases. We believe that the results presented in this paper are novel and will be beneficial in encouraging future research in this field.https://doi.org/10.1186/s13660-023-02952-yConvex functionsExponentially convex functionsHermite–Hadamard inequalitiesRiemann–Liouville fractional integrals |
| spellingShingle | Jaya Bisht Nidhi Sharma Shashi Kant Mishra Abdelouahed Hamdi Some new integral inequalities for higher-order strongly exponentially convex functions Journal of Inequalities and Applications Convex functions Exponentially convex functions Hermite–Hadamard inequalities Riemann–Liouville fractional integrals |
| title | Some new integral inequalities for higher-order strongly exponentially convex functions |
| title_full | Some new integral inequalities for higher-order strongly exponentially convex functions |
| title_fullStr | Some new integral inequalities for higher-order strongly exponentially convex functions |
| title_full_unstemmed | Some new integral inequalities for higher-order strongly exponentially convex functions |
| title_short | Some new integral inequalities for higher-order strongly exponentially convex functions |
| title_sort | some new integral inequalities for higher order strongly exponentially convex functions |
| topic | Convex functions Exponentially convex functions Hermite–Hadamard inequalities Riemann–Liouville fractional integrals |
| url | https://doi.org/10.1186/s13660-023-02952-y |
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