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
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.
