Some universal nonlinear inequalities

TL;DR

This paper introduces new universal nonlinear inequalities based on a monotone measure integral, generalizing classical inequalities like Chebyshev, Minkowski, and Holder to a broader measurable space context.

Contribution

It develops generalized versions of key inequalities using a monotone measure-based integral, extending prior results in the field.

Findings

New inequalities generalize classical results

Applicable to arbitrary measurable spaces

Enhance the theoretical framework of nonlinear inequalities

Abstract

In this paper, new versions of Chebyshev's, Minkowski's and Holder's type inequalities are studied by using a monotone measure-base universal integral on an arbitrary measurable space. This paper generalizes some previous results obtained by many researchers.