Refinements of the Converse Hölder and Minkowski Inequalities

Abstract

We give a refinement of the converse Hölder 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.

Keywords

• Beckenbach’s inequality
• converse inequality
• Hölder’s inequality
• mean
• Minkowski’s inequality
• mixed mean