A Class Of Nonlinear Operator Fixed Point Theorem,

The existence and uniqueness of fixed points for a class of mixed monotone operators without assuming continuous or compact have been discussed in the real Banach space, by using the partial ordering theory and monotone iteration method. It is also analysised the existence and uniqueness of this operators equations.The full text divided into four chapters .Fundamental knowledge,concept and research summary of mixed monotone operators have been provided in chapter 1.In chapter 2 ,the existence and uniqueness of fixed points for this operator are obtained by using the cone theory and monotone iteration method in the general condition.The existence and uniqueness of solutions for a class of mixed monotone operators equations have been studied in the real Banach space , the error estimate also given in chapter 3. The results have been improved some results are obtained.In chapter 4 ,fixed points of mixed monotone operators were further investigated, the existence and uniqueness theorem of fixed points for this operators with affine perturbation was got.