Research On Some Nonlinear Operator Problems In Metric Space

Recently,nonlinear operator problems have become a hot research topic.In this paper,we introduce some new concepts on the basis of metric spaces.Through the study on some problems of nonlinear operator problems in metric space,we establish some new theorems.In this paper we mainly study some solutions of Nonlinear Operator Equations in some extension of metric space.And as an application of the main conclusions of this paper,the rationality of the several specific examples is given to verify the results.The thesis is divided into four chapters.The main contents of each chapter are gives as follows:In chapter one,we briefly introduce the development process of the metric space and some related basic theoretical knowledge,and analyze the current development situation of metric space.In chapter two,on the basis of the complete Menger PGM-space,the condition of the ?-?-type of contraction operator is weakened,and a new fixed point theorem is obtained.Finally,an example is given to illustrate the rationality of our conclusion.In chapter three,on the basis of the complete Menger PTM-space,by using the properties of ?-functions and H-functions,and a new multiple fixed point theorem is obtained.Finally,an example is given to illustrate the rationality of our results.In chapter four,on the basis of the complete CVM-space,by introducing partial order in CVM-space,we obtain a new fixed point theorem of nonlinear fixed point theorem.