{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,14]],"date-time":"2026-02-14T06:05:37Z","timestamp":1771049137145,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T00:00:00Z","timestamp":1770854400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The Minkowski and H\u00f6lder inequalities play an important role in many areas of pure and applied mathematics, such as Convex Analysis, Probabilities, Control Theory, Fixed Point theorems, and Mathematical Economics. Also, non-additive measures, non-additive integrals and set-valued integrals are useful tools in several areas of theoretical and applied mathematics. In this paper we present and prove some H\u00f6lder and Minkowski inequality (or reverse inequality) types obtained for Birkhoff weak integrable functions with respect to a non-additive measure. Then, we apply these results to the interval-valued case.<\/jats:p>","DOI":"10.3390\/axioms15020133","type":"journal-article","created":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T12:05:46Z","timestamp":1770897946000},"page":"133","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Some Reverse Inequalities for Scalar Birkhoff Weak Integrable Functions"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8180-3590","authenticated-orcid":false,"given":"Anca","family":"Croitoru","sequence":"first","affiliation":[{"name":"Faculty of Mathematics, University \u201dAlexandru Ioan Cuza\u201d, Bd. Carol I, No. 11, 700506 Ia\u015fi, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0144-8811","authenticated-orcid":false,"given":"Alina","family":"Iosif","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Information Technology, Mathematics and Physics, Petroleum-Gas University of Ploie\u015fti, Bd. Bucure\u015fti, No. 39, 100680 Ploie\u015fti, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0161-8729","authenticated-orcid":false,"given":"Anna Rita","family":"Sambucini","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Sciences, University of Perugia, 1, Via Vanvitelli, 06123 Perugia, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6047-2646","authenticated-orcid":false,"given":"Luca","family":"Zampogni","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Sciences, University of Perugia, 1, Via Vanvitelli, 06123 Perugia, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"979","DOI":"10.1093\/mnras\/85.9.979","article-title":"Note on Rosseland\u2019s integral for the stellar absorption coefficient","volume":"85","author":"Milne","year":"1925","journal-title":"Mon. Not. R. Astron. 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