Majorization-Type Integral Inequalities Related to a Result of Bennett with Applications
In this paper, starting from abstract versions of a result of Bennett given by Niculescu, we derive new majorization-type integral inequalities for convex functions using finite signed measures. The proof of the main result is based on a generalization of a recently discovered majorization-type inte...
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MDPI AG
2025-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/10/1563 |
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| author | László Horváth |
| author_facet | László Horváth |
| author_sort | László Horváth |
| collection | DOAJ |
| description | In this paper, starting from abstract versions of a result of Bennett given by Niculescu, we derive new majorization-type integral inequalities for convex functions using finite signed measures. The proof of the main result is based on a generalization of a recently discovered majorization-type integral inequality. As applications of the results, we give simple proofs of the integral Jensen and Lah–Ribarič inequalities for finite signed measures, generalize and extend known results, and obtain an interesting new refinement of the Hermite–Hadamard–Fejér inequality. |
| format | Article |
| id | doaj-art-05b8903496334f0fae936fdf03a2b27b |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-05b8903496334f0fae936fdf03a2b27b2025-08-20T01:56:32ZengMDPI AGMathematics2227-73902025-05-011310156310.3390/math13101563Majorization-Type Integral Inequalities Related to a Result of Bennett with ApplicationsLászló Horváth0Department of Mathematics, University of Pannonia, Egyetem u. 10, 8200 Veszprém, HungaryIn this paper, starting from abstract versions of a result of Bennett given by Niculescu, we derive new majorization-type integral inequalities for convex functions using finite signed measures. The proof of the main result is based on a generalization of a recently discovered majorization-type integral inequality. As applications of the results, we give simple proofs of the integral Jensen and Lah–Ribarič inequalities for finite signed measures, generalize and extend known results, and obtain an interesting new refinement of the Hermite–Hadamard–Fejér inequality.https://www.mdpi.com/2227-7390/13/10/1563convex functionssigned measuresSteffensen–Popoviciu and dual Steffensen–Popoviciu measuresintegral Jensen and Lah–Ribarič inequalitiesHermite–Hadamard–Fejér inequality |
| spellingShingle | László Horváth Majorization-Type Integral Inequalities Related to a Result of Bennett with Applications Mathematics convex functions signed measures Steffensen–Popoviciu and dual Steffensen–Popoviciu measures integral Jensen and Lah–Ribarič inequalities Hermite–Hadamard–Fejér inequality |
| title | Majorization-Type Integral Inequalities Related to a Result of Bennett with Applications |
| title_full | Majorization-Type Integral Inequalities Related to a Result of Bennett with Applications |
| title_fullStr | Majorization-Type Integral Inequalities Related to a Result of Bennett with Applications |
| title_full_unstemmed | Majorization-Type Integral Inequalities Related to a Result of Bennett with Applications |
| title_short | Majorization-Type Integral Inequalities Related to a Result of Bennett with Applications |
| title_sort | majorization type integral inequalities related to a result of bennett with applications |
| topic | convex functions signed measures Steffensen–Popoviciu and dual Steffensen–Popoviciu measures integral Jensen and Lah–Ribarič inequalities Hermite–Hadamard–Fejér inequality |
| url | https://www.mdpi.com/2227-7390/13/10/1563 |
| work_keys_str_mv | AT laszlohorvath majorizationtypeintegralinequalitiesrelatedtoaresultofbennettwithapplications |