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 Holder 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 Holder inequalities.