On some classical integral inequalities in the setting of new post quantum integrals

Abstract

In this article, we introduce the notion of $ _{a}{\bar{T}}_{p,q} $-integrals. Using the definition of $ _{a}{\bar{T}}_{p,q} $-integrals, we derive some new post quantum analogues of some classical results of Young's inequality, Hölder's inequality, Minkowski's inequality, Ostrowski's inequality and Hermite-Hadamard's inequality.

Keywords

• convex functions
• $ _{a}{\bar{t}}_{p，q} $-integral
• young's inequality
• hölder's inequality
• minkowski's inequality
• ostrowski's inequality
• hermite-hadamard's inequality