On the refinements of some important inequalities via ( p , q ) $(p,q)$ -calculus and their applications

Abstract

Abstract We establish some interesting refinements of the ( p , q ) $(p,q)$ -Hölder integral inequality and the ( p , q ) $(p,q)$ -power-mean integral inequality. As applications, we show that some existing ( p , q ) $(p,q)$ -integral inequalities can be improved by the results obtained in this paper.

Keywords

• ( p , q ) $(p,q)$ -integral inequalities
• Hermite–Hadamard inequality
• Convex mappings