Some reverse inequalities for scalar Birkhoff weak integrable functions

TL;DR

This paper establishes new inequalities and their reverses for scalar Birkhoff weak integrable functions under non-additive measures, extending classical integral inequalities to a broader context.

Contribution

It introduces novel reverse inequalities for scalar Birkhoff weak integrable functions with respect to non-additive measures, expanding the theoretical framework of integral inequalities.

Findings

Derived new inequalities for Birkhoff weak integrable functions

Established reverse inequalities extending classical Hölder and Minkowski inequalities

Applied results to functions with respect to non-additive measures

Abstract

Some inequalities and reverses of classic H\"{o}lder and Minkowski types are obtained for scalar Birkhoff weak integrable functions with respect to a non-additive measure.