On Some Operator Inequalities

In this dissertation, we mainly consider the refinements of some operator inequalities.We intend to seperate this dissertation into four sections.In the first section, we introduce some related inequalities and background. Besides,some theorems and knowledge are also introduced.In the second section, we consider the refined Young inequality with Kantorovich con-stant, which is the further extension of the result of S. Furuichi. And some nice refinementsof arithmatic-geomitric mean are obtained in diference form.In the third section, we talk about the diferences between power means associated todiferent sequences of weights. The general extensions of the results of A. L. Aldaz andsome applications to operator A-G-H inequalities are also given.In the fourth section, we focus on some notes on Jensen inequality and the propertiesof Jensen operator.