A Generalization Of Fixed Point Theorem On The Cone’s Definition

This paper considers the fixed point theorem of the cone metric space, We first introduce the cone definition and defines some properties of cone.The fixed point theorem of significance lies not only in the theory of differential equations.It is widely used in the control theory, nonlinear analysis and a wide range of analysis field. In addition to the introduction of the fixed point theorem and some important theorems, We primarily promote the fixed point theorem in the cone metric spaces.and give some fixed point theorems of compression mapping and Ekeland variational principle also exists in several forms, Ekeland variational principle is also the conclusions in the cone under conditions of complete space.