Mapping Iteration And Continuous Convex Solutions Of Iterative Equations

Iteration means the same operation or the same repeat operation,iterative equation is based on iterative arithmetic in the form of equation,the iterative equation and differential equation and integral equation,the close power system.But the iterative operator is an operator which is obviously complicated by an analogous differential operator,which can be divided into two categories:linear function iteration and nonlinear function iteration.Polynomial iterative equation and.Aiming at linear function iteration,tend to find out all of the continuous solution,and the nonlinear function iteration,the Schauder-Tychonoff's method of fixed point theorem The existence,uniqueness and stability of the root of the iterative equation are analyzed.In the topological vector space,this paper USES schauder-tychonoff's fixed point theorem to prove the existence of solutions to the iterative equations on the non-compact interval and find the non-single mediation.The full text is divided into two parts:In the first part,the iterative operator is studied.Using Matlab tools to linear function simulation,the effect of iterative and nonlinear function iteration first studied the piecewise function iteration problem,every segment is a piecewise function characteristics of the interval of the results is very complete.Piecewise function,this paper discusses the features of interval iteration,in turn,study of linear function iterative and nonlinear function iteration,and gives the change law of conclusion and non-monotone points.In the second part,we study the solution of polynomial iterative equations in topo-logical vector space.Firstly,we discuss the existence problem of the solution of the linear space of the Hausdorff topological line,and find out the non-single mediation in the ex-istence of solutions.In this paper,we discuss the convexity of the solution according to the schauder-tychonoff fixed point theorem,and then expand the discussion of convexity.