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

Some Inequalities involving Heron and Heinz Means of two Convex Functionals