Necessary and sufficient conditions for discrete inequalities of Jensen–Steffensen type with applications
Abstract In this paper we give a necessary and sufficient condition for the discrete Jensen inequality to be satisfied for real (not necessarily nonnegative) weights. The result generalizes and completes the classical Jensen–Steffensen inequality. The validity of the strict inequality is studied. As...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-023-03073-2 |
| _version_ | 1797362799682256896 |
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| author | László Horváth |
| author_facet | László Horváth |
| author_sort | László Horváth |
| collection | DOAJ |
| description | Abstract In this paper we give a necessary and sufficient condition for the discrete Jensen inequality to be satisfied for real (not necessarily nonnegative) weights. The result generalizes and completes the classical Jensen–Steffensen inequality. The validity of the strict inequality is studied. As applications, we first give the form of our result for strongly convex functions, then we study discrete quasi-arithmetic means with real (not necessarily nonnegative) weights, and finally we refine the inequality obtained. |
| first_indexed | 2024-03-08T16:12:39Z |
| format | Article |
| id | doaj.art-b8d0895d9890482f8bb554fe5f9dc5d0 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-03-08T16:12:39Z |
| publishDate | 2024-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-b8d0895d9890482f8bb554fe5f9dc5d02024-01-07T12:53:35ZengSpringerOpenJournal of Inequalities and Applications1029-242X2024-01-012024111610.1186/s13660-023-03073-2Necessary and sufficient conditions for discrete inequalities of Jensen–Steffensen type with applicationsLászló Horváth0Department of Mathematics, University of PannoniaAbstract In this paper we give a necessary and sufficient condition for the discrete Jensen inequality to be satisfied for real (not necessarily nonnegative) weights. The result generalizes and completes the classical Jensen–Steffensen inequality. The validity of the strict inequality is studied. As applications, we first give the form of our result for strongly convex functions, then we study discrete quasi-arithmetic means with real (not necessarily nonnegative) weights, and finally we refine the inequality obtained.https://doi.org/10.1186/s13660-023-03073-2Convex and strongly convex functionsDiscrete Jensen–Steffensen inequalityQuasi-arithmetic meansRefinement |
| spellingShingle | László Horváth Necessary and sufficient conditions for discrete inequalities of Jensen–Steffensen type with applications Journal of Inequalities and Applications Convex and strongly convex functions Discrete Jensen–Steffensen inequality Quasi-arithmetic means Refinement |
| title | Necessary and sufficient conditions for discrete inequalities of Jensen–Steffensen type with applications |
| title_full | Necessary and sufficient conditions for discrete inequalities of Jensen–Steffensen type with applications |
| title_fullStr | Necessary and sufficient conditions for discrete inequalities of Jensen–Steffensen type with applications |
| title_full_unstemmed | Necessary and sufficient conditions for discrete inequalities of Jensen–Steffensen type with applications |
| title_short | Necessary and sufficient conditions for discrete inequalities of Jensen–Steffensen type with applications |
| title_sort | necessary and sufficient conditions for discrete inequalities of jensen steffensen type with applications |
| topic | Convex and strongly convex functions Discrete Jensen–Steffensen inequality Quasi-arithmetic means Refinement |
| url | https://doi.org/10.1186/s13660-023-03073-2 |
| work_keys_str_mv | AT laszlohorvath necessaryandsufficientconditionsfordiscreteinequalitiesofjensensteffensentypewithapplications |