Some Inequalities involving Heron and Heinz Means of two Convex Functionals

TL;DR

This paper introduces Heron and Heinz means for convex functionals, explores related inequalities, and derives new operator inequalities and refinements using a functional approach.

Contribution

It presents the first definitions of Heron and Heinz means for convex functionals and develops new inequalities and refinements for operator inequalities.

Findings

Established inequalities involving Heron and Heinz means of convex functionals.

Derived operator inequalities from the functional results.

Provided new refinements of existing operator inequalities.

Abstract

In this paper we first introduce the Heron and Heinz means of two convex functionals. Afterwards, some inequalities involving these functional means are investigated. The operator versions of our theoretical functional results are immediately deduced. We also obtain new refinements of some known operator inequalities via our functional approach in a fast and nice way.