Classical inequalities for pseudo-integral

TL;DR

This paper extends classical inequalities like Young's, H"older's, Minkowski's, and Hermite-Hadamard to the pseudo-integral ($g$-integral), including refinements and special cases, broadening their applicability.

Contribution

It introduces new versions of key inequalities for the pseudo-integral, covering various cases and providing refinements and special case derivations.

Findings

Derived Young's, H"older's, Minkowski's, Hermite-Hadamard inequalities for $g$-integral.

Provided refinements for Hermite-Hadamard inequality.

Established $g$-analogue of geometric-logarithmic-arithmetic inequality.

Abstract

In this paper, we have derived certain classical inequalities, namely, Young's, H\"older's, Minkowski's and Hermite-Hadamard inequalities for pseudo-integral (also known as $g$-integral). For Young's, H\"older's, Minkowski's inequalities, both the cases $p>1$ as well as $p<1,\,p\ne 0$ have been covered. Moreover, in the case of Hermite-Hadamard inequality, a refinement has also been proved and as a special case, $g$-analogue of geometric-logarithmic-arithmetic inequality has been deduced.