The Discussion Of The Solution To Several Nonlinear Operator Equations And Systems Of Operator Equations

In this article,by using the cone theory and partial ordering method,the existence and uniqueness of solutions for some kinds of systems of two binary operator equations are disscussed in the Banach space,and the error estimations for the convergent iterative sequence are given.So the fixed point of decreasing operator are also disscussed.Some new rescults are obtained.The main contents of this paper is as follows:In the first chapter,the real background,the research significance,the results about the research to the nonlinear operator by using the partial ordering method and the main new work of this article are showed.In the second chapter,by using the cone theory and non-monotone iterative technique,the the existence and uniqueness of solutions for some kinds of nonlinear non-monotone systems of two binary operator equations are gained,also the convergent iterative sequence and the error estimations are obtained.In the third chapter,by using the cone theory and monotone iterative technique, the the existence and uniqueness of solutions for some kinds of nonlinear monotone systems of two binary operator equations are gained,also the convergent iterative sequence and the error estimations are obtained.In the forth chapter,by generation and application two fixed point theory about decreasing operator,two fixed point theory about non-decreasing operator are obtained.