Refinements of the Converse Holder and Minkowski Inequalities

We give a refinement of the converse Holder inequality for functionals using an interpolation result for Jensen's inequality. Additionally, we obtain similar improvements of the converse of the Beckenbach inequality. We consider the converse Minkowski inequality for functionals and of its continuous form and give refinements of it. Application on integral mixed means is given.

Automated summary

We provide a refinement of the converse Holder inequality for functionals by using an interpolation result for Jensen's inequality. In addition, we improve the converse of the Beckenbach inequality. We also consider the converse Minkowski inequality for functionals and give refinements of it, along with applications on integral mixed means.