Refinements of the Converse Hölder and Minkowski Inequalities

We give a refinement of the converse Hölder inequality for functionals using an interpola-tion 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. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.