The Generalized Furuta Type Inequalities And Related Monotonicity Of Operator Function

In this paper, we are based on the Furuta inequality and its generalization and shallintroduce multiple operators on chaotic order and talk about related monotonicity andequivalence of operator functions. In order to introduce the correlative problems, we dividethis paper into three parts.The frst part is introduction. We mainly introduce reseach background related toFuruta inequality Furuta type inequality and so on. In addition, we also introduce sometheorems and knowledge that are referred frequently in this paper.The second part is some operator inequalities on chaotic order and related monotonic-ity of operator functions. This part is separated into two small parts to introduce, whichstudies operator inequalities of Fututa type about several perators. We briefly prove theseoperator inequalities and also talk about related monotonicity of operator functions.The fnal part is genalized Furuta type inequality and an equivalence between opera-tor inequalities and operator functions. This part extend the content about two operators,and make foundation for studying sevral noncommutative operators.