The Fixed Point Theorem Of A Class Of Nonlinear Operators

In this thesis,we investigate some properties of ordered set and relevant cone by method of partially ordered in Banach spaces.Where the relation of ordered is de-rived from a nonzero continuous linear functional.And we study fixed points'existence of some nonlinear operators by these properties in Banach spaces.The whole thesis is divided into three chapters.In the first chapter,we introduce the relative background of the fixed point theory of nonlinear operator,development and the main results of this paper.In the second chapter,we construct partially ordered and cone by a nonzero linear continuous functional,and explore their some properties.In the third chapter,firstly,we study the coupled fixed point's existence of mixed monotone operator from properties in the second chapter.Secondly,we discuss the existence and uniqueness of fixed point for nonlinear operator F and the convergence of iterative ordered.Where F satisfy:...