New Young-type integral inequalities using composition schemes

This article presents new results that extend the scope of the Young integral inequality. They are formulated by different functional composition schemes of the integrals involved. These schemes depend on a unique auxiliary function. In total, six theorems are proved. Four of them are derived from a simple composition scheme based on sub-additive, super-additive, convex and concave properties of the auxiliary function, while the remaining two use more sophisticated composition schemes based on convex and concave properties. Our framework also unifies several established variants of the Young integral inequality. Three secondary propositions complete the theorems. The theory is supported by a number of tractable examples involving power, exponential, logarithmic, ratio and hyperbolic functions.