Sharp Companion Inequalities For Some Classical Means

The study of inequalities is an important branch in analysis. Various means andtheir optimal estimates have wide applications in physics, mechanics, economics andmanagements. This paper deals with some classical means and their relations. We firstgive a sufcient condition ensuring companion optimal inequalities, and then we obtainsome optimal estimates related to some means such as Stolarsky mean, power mean andgeneralized Heronian mean. These inequalities are generalizations of the known results,and are of application value.