New estimates on generalized Hermite–Hadamard–Mercer-type inequalities
Abstract The concept of a convex function plays a crucial role in fields of mathematical analysis and inequality theory. The importance of convex functions is exemplified by Mercer’s inequality. This inequality, which is derived through the application of convex functions, has been extensively studi...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-02-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-025-02012-y |
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| _version_ | 1850087171265921024 |
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| author | Çetin Yıldız Samet Erden Seth Kermausuor Daniel Breaz Luminiţa-Ioana Cotîrlă |
| author_facet | Çetin Yıldız Samet Erden Seth Kermausuor Daniel Breaz Luminiţa-Ioana Cotîrlă |
| author_sort | Çetin Yıldız |
| collection | DOAJ |
| description | Abstract The concept of a convex function plays a crucial role in fields of mathematical analysis and inequality theory. The importance of convex functions is exemplified by Mercer’s inequality. This inequality, which is derived through the application of convex functions, has been extensively studied and is a subject of considerable interest within the mathematical community. This paper presents new generalizations related to Mercer’s inequality and compares the inequalities obtained for different values of n with those presented in the existing literature. Also, this study presents pioneering contributions to the field, and we believe that the results in this study will enhance further research on the topic. |
| format | Article |
| id | doaj-art-cb3f95412e104dc5a7bcb313728014a0 |
| institution | DOAJ |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-cb3f95412e104dc5a7bcb313728014a02025-08-20T02:43:16ZengSpringerOpenBoundary Value Problems1687-27702025-02-012025112010.1186/s13661-025-02012-yNew estimates on generalized Hermite–Hadamard–Mercer-type inequalitiesÇetin Yıldız0Samet Erden1Seth Kermausuor2Daniel Breaz3Luminiţa-Ioana Cotîrlă4Deparment of Mathematics, K.K. Education Faculty, Atatürk UniversityDepartment of Mathematics, Faculty of Science, Bartın UniversityDepartment of Mathematics and Computer Science, Alabama State UniversityDepartment of Mathematics, 1 Decembrie University of Alba-IuliaDepartment of Mathematics, Technical University of Cluj-NapocaAbstract The concept of a convex function plays a crucial role in fields of mathematical analysis and inequality theory. The importance of convex functions is exemplified by Mercer’s inequality. This inequality, which is derived through the application of convex functions, has been extensively studied and is a subject of considerable interest within the mathematical community. This paper presents new generalizations related to Mercer’s inequality and compares the inequalities obtained for different values of n with those presented in the existing literature. Also, this study presents pioneering contributions to the field, and we believe that the results in this study will enhance further research on the topic.https://doi.org/10.1186/s13661-025-02012-yConvex functionMercer inequalityHermite–Hadamard inequalityJensen inequality |
| spellingShingle | Çetin Yıldız Samet Erden Seth Kermausuor Daniel Breaz Luminiţa-Ioana Cotîrlă New estimates on generalized Hermite–Hadamard–Mercer-type inequalities Boundary Value Problems Convex function Mercer inequality Hermite–Hadamard inequality Jensen inequality |
| title | New estimates on generalized Hermite–Hadamard–Mercer-type inequalities |
| title_full | New estimates on generalized Hermite–Hadamard–Mercer-type inequalities |
| title_fullStr | New estimates on generalized Hermite–Hadamard–Mercer-type inequalities |
| title_full_unstemmed | New estimates on generalized Hermite–Hadamard–Mercer-type inequalities |
| title_short | New estimates on generalized Hermite–Hadamard–Mercer-type inequalities |
| title_sort | new estimates on generalized hermite hadamard mercer type inequalities |
| topic | Convex function Mercer inequality Hermite–Hadamard inequality Jensen inequality |
| url | https://doi.org/10.1186/s13661-025-02012-y |
| work_keys_str_mv | AT cetinyıldız newestimatesongeneralizedhermitehadamardmercertypeinequalities AT sameterden newestimatesongeneralizedhermitehadamardmercertypeinequalities AT sethkermausuor newestimatesongeneralizedhermitehadamardmercertypeinequalities AT danielbreaz newestimatesongeneralizedhermitehadamardmercertypeinequalities AT luminitaioanacotirla newestimatesongeneralizedhermitehadamardmercertypeinequalities |