On Some Operator Inequalities

In this dissertation, we mainly consider the refnements of some operator inequalities.We intend to seperate this dissertation into three sections.In the frst section, we introduce some related inequalities and background. Besides,some theorems and knowledge are also known.In the second section, we establish optimal upper bound for Jensen operator by meansof discrete Jensen’s functional. Based on this, we obtain the reverse weighted arithmetic-geometric operator mean inequalities in which coefcents are more accurate. Furthermore,by the same method we obtain other generalized Young inequalities.In the third section, we improve the inequalities introduced by Fujii, et al. to somerefned operator inequalities of covariance-variance by which the Kantorovich inequalitiesare extended.