Inequalities and majorisations for the Riemann-Stieltjes integral on time scales

TL;DR

This paper extends inequalities related to the Riemann-Stieltjes integral to the framework of time scales, unifying continuous and discrete analysis.

Contribution

It generalizes existing inequalities to the time scales setting using Riemann-Stieltjes delta integrals, broadening their applicability.

Findings

Established dynamic inequalities of majorisation type on time scales

Unified continuous and discrete cases under a common framework

Extended previous results to a more general setting

Abstract

We prove dynamic inequalities of majorisation type for functions on time scales. The results are obtained using the notion of Riemann-Stieltjes delta integral and give a generalization of [App. Math. Let. 22 (2009), no. 3, 416--421] to time scales.