Some Generalizations Of Fixed Point Theorems In Cone Metric Spaces

Since the notation of cone metric spaces was raised, many authors have studied its constructions and properties. The results on the existence of fixed points of generalized contractive mappings were extended by relaxing the contractive conditions. The obtained results extend the recent relative results and the classical theorems in metric spaces.This paper is mainly composed of three chapters:Chapter1is the introduction. We introduce the development of the fixed point of nonlinear operator theory in cone metric spaces.Chapter2is based on the definition of a special function and the concept of comparable, thus the fixed point theorems in metric spaces have been generalized to the cone metric spaces.In chapter3, with the cone theory and monotone iterative technique, this section mainly investigates the existence and uniqueness of the fixed point of the generalized contractive mappings by constructing the sequence ｛xn｝:xn+1=axn+bTxn|a+b,n=0,1,2, and then presents several now fixed point theorems.