Some Research Of Young Inequality And Operator Mean Inequality

Operator theory is an important part of the theory of functional analysis,arising in early twentieth century.It has applied in many areas,such as:matrix theory,control theory,statistics and so on.As a part of operator theory,Young inequality is simple but important.And it has attracted many researchers in the field,where adding a positive term to the left side is possible.In recent decades,more and more results about Young inequality are presented.Fol-lowing this way,we can do further work on it.In this work,we mainly give refinements and reverses of Young and Young type in-equality.Besides,some results of Heron mean and harmonic-geometric-arithmetic mean are presented too.The main work contains the following topics:1.We prove several multi-term refinements of Young and Young type inequalities with Kantorovich constant for both real numbers and matrices.Then,we will give the refinements of Young inequalities for operators and matrix with a different method based on others' results.2.The relationship between Heron mean and arithmetic-geometry-harmonic mean are studied,and some results about Heron mean are given.3.Some results of harmonic-geometric-arithmetic mean will be improved and inequal-ities in the form of operators,matrices and determinants corresponding to them are given.