Inequalities in Riemann–Lebesgue Integrability

Anca Croitoru (), Alina Gavriluţ, Alina Iosif and Anna Rita Sambucini
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Anca Croitoru: Faculty of Mathematics, University “Alexandru Ioan Cuza”, Bd. Carol I, No. 11, 700506 Jassy, Romania
Alina Gavriluţ: Faculty of Mathematics, University “Alexandru Ioan Cuza”, Bd. Carol I, No. 11, 700506 Jassy, Romania
Alina Iosif: Department of Computer Science, Information Technology, Mathematics and Physics, Petroleum-Gas University of Ploieşti, Bd. Bucureşti, No. 39, 100680 Ploieşti, Romania
Anna Rita Sambucini: Department of Mathematics and Computer Sciences, University of Perugia, 1, Via Vanvitelli, 06123 Perugia, Italy

Mathematics, 2023, vol. 12, issue 1, 1-12

Abstract: 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.

Keywords: Riemann–Lebesgue integral; interval-valued (set) multifunction; non-additive set function; Hölder-type inequality; Minkowski-type inequality; Beckenbach-type inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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