Inequalities in Riemann–Lebesgue Integrability
In this paper, we prove some inequalities for Riemann–Lebesgue integrable functions when the considered integration is obtained via a non-additive measure, including the reverse Hölder inequality and the reverse Minkowski inequality. Then, we generalize these inequalities to the framework of a multi...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/1/49 |
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| author | Anca Croitoru Alina Gavriluţ Alina Iosif Anna Rita Sambucini |
| author_facet | Anca Croitoru Alina Gavriluţ Alina Iosif Anna Rita Sambucini |
| author_sort | Anca Croitoru |
| collection | DOAJ |
| description | In this paper, we prove some inequalities for Riemann–Lebesgue integrable functions when the considered integration is obtained via a non-additive measure, including the reverse Hölder inequality and the reverse Minkowski inequality. Then, we generalize these inequalities to the framework of a multivalued case, in particular for Riemann–Lebesgue integrable interval-valued multifunctions, and obtain some inequalities, such as a Minkowski-type inequality, a Beckenbach-type inequality and some generalizations of Hölder inequalities. |
| first_indexed | 2024-03-08T15:02:14Z |
| format | Article |
| id | doaj.art-3d64c77688d746dcae2461a3cc11e792 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-08T15:02:14Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-3d64c77688d746dcae2461a3cc11e7922024-01-10T15:03:25ZengMDPI AGMathematics2227-73902023-12-011214910.3390/math12010049Inequalities in Riemann–Lebesgue IntegrabilityAnca Croitoru0Alina Gavriluţ1Alina Iosif2Anna Rita Sambucini3Faculty of Mathematics, University “Alexandru Ioan Cuza”, Bd. Carol I, No. 11, 700506 Jassy, RomaniaFaculty of Mathematics, University “Alexandru Ioan Cuza”, Bd. Carol I, No. 11, 700506 Jassy, RomaniaDepartment of Computer Science, Information Technology, Mathematics and Physics, Petroleum-Gas University of Ploieşti, Bd. Bucureşti, No. 39, 100680 Ploieşti, RomaniaDepartment of Mathematics and Computer Sciences, University of Perugia, 1, Via Vanvitelli, 06123 Perugia, ItalyIn this paper, we prove some inequalities for Riemann–Lebesgue integrable functions when the considered integration is obtained via a non-additive measure, including the reverse Hölder inequality and the reverse Minkowski inequality. Then, we generalize these inequalities to the framework of a multivalued case, in particular for Riemann–Lebesgue integrable interval-valued multifunctions, and obtain some inequalities, such as a Minkowski-type inequality, a Beckenbach-type inequality and some generalizations of Hölder inequalities.https://www.mdpi.com/2227-7390/12/1/49Riemann–Lebesgue integralinterval-valued (set) multifunctionnon-additive set functionHölder-type inequalityMinkowski-type inequalityBeckenbach-type inequality |
| spellingShingle | Anca Croitoru Alina Gavriluţ Alina Iosif Anna Rita Sambucini Inequalities in Riemann–Lebesgue Integrability Mathematics Riemann–Lebesgue integral interval-valued (set) multifunction non-additive set function Hölder-type inequality Minkowski-type inequality Beckenbach-type inequality |
| title | Inequalities in Riemann–Lebesgue Integrability |
| title_full | Inequalities in Riemann–Lebesgue Integrability |
| title_fullStr | Inequalities in Riemann–Lebesgue Integrability |
| title_full_unstemmed | Inequalities in Riemann–Lebesgue Integrability |
| title_short | Inequalities in Riemann–Lebesgue Integrability |
| title_sort | inequalities in riemann lebesgue integrability |
| topic | Riemann–Lebesgue integral interval-valued (set) multifunction non-additive set function Hölder-type inequality Minkowski-type inequality Beckenbach-type inequality |
| url | https://www.mdpi.com/2227-7390/12/1/49 |
| work_keys_str_mv | AT ancacroitoru inequalitiesinriemannlebesgueintegrability AT alinagavrilut inequalitiesinriemannlebesgueintegrability AT alinaiosif inequalitiesinriemannlebesgueintegrability AT annaritasambucini inequalitiesinriemannlebesgueintegrability |