Bellman–Steffensen type inequalities
Abstract In this paper some Bellman–Steffensen type inequalities are generalized for positive measures. Using sublinearity of a class of convex functions and Jensen’s inequality, nonnormalized versions of Steffensen’s inequality are obtained. Further, linear functionals, from obtained Bellman–Steffe...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-10-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-018-1882-9 |
| _version_ | 1818175521835450368 |
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| author | Julije Jakšetić Josip Pečarić Ksenija Smoljak Kalamir |
| author_facet | Julije Jakšetić Josip Pečarić Ksenija Smoljak Kalamir |
| author_sort | Julije Jakšetić |
| collection | DOAJ |
| description | Abstract In this paper some Bellman–Steffensen type inequalities are generalized for positive measures. Using sublinearity of a class of convex functions and Jensen’s inequality, nonnormalized versions of Steffensen’s inequality are obtained. Further, linear functionals, from obtained Bellman–Steffensen type inequalities, are produced and their action on families of exponentially convex functions is studied. |
| first_indexed | 2024-12-11T20:01:37Z |
| format | Article |
| id | doaj.art-d3ae317271724eccb2f1437e3f11a880 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-11T20:01:37Z |
| publishDate | 2018-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-d3ae317271724eccb2f1437e3f11a8802022-12-22T00:52:31ZengSpringerOpenJournal of Inequalities and Applications1029-242X2018-10-012018111510.1186/s13660-018-1882-9Bellman–Steffensen type inequalitiesJulije Jakšetić0Josip Pečarić1Ksenija Smoljak Kalamir2Faculty of Mechanical Engineering and Naval Architecture, University of ZagrebFaculty of Textile Technology, University of ZagrebFaculty of Textile Technology, University of ZagrebAbstract In this paper some Bellman–Steffensen type inequalities are generalized for positive measures. Using sublinearity of a class of convex functions and Jensen’s inequality, nonnormalized versions of Steffensen’s inequality are obtained. Further, linear functionals, from obtained Bellman–Steffensen type inequalities, are produced and their action on families of exponentially convex functions is studied.http://link.springer.com/article/10.1186/s13660-018-1882-9Steffensen’s inequalityBellman–Steffensen type inequalityMeasure theoryExponential convexity |
| spellingShingle | Julije Jakšetić Josip Pečarić Ksenija Smoljak Kalamir Bellman–Steffensen type inequalities Journal of Inequalities and Applications Steffensen’s inequality Bellman–Steffensen type inequality Measure theory Exponential convexity |
| title | Bellman–Steffensen type inequalities |
| title_full | Bellman–Steffensen type inequalities |
| title_fullStr | Bellman–Steffensen type inequalities |
| title_full_unstemmed | Bellman–Steffensen type inequalities |
| title_short | Bellman–Steffensen type inequalities |
| title_sort | bellman steffensen type inequalities |
| topic | Steffensen’s inequality Bellman–Steffensen type inequality Measure theory Exponential convexity |
| url | http://link.springer.com/article/10.1186/s13660-018-1882-9 |
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