The Extension And Proof Of Several Kinds Of Fixed Point Theorems

In mathematics,the fixed point theorem is an important part in functional analysis.In fact,the fixed point theorem is the problem of solving the operator equation Tx=x.It is very important to study the existence and uniqueness of the solution of the differential equation and integral equation.And it is easily verifiable.This paper is divided into four parts The first chapter introduces the classification and development of fixed point and fixed point theorem.In the second chapter,starting from the conditions of the fixed point theorem,we use the method of limit iteration to generalize it to a class of generalized fixed point theorems.We obtain a generalized form of the fixed point theorem and introduce its solution.The application of integral equations in the existence and uniqueness of the integral equations further highlights the generalization of the fixed point theorem and its application.The third chapter we mainly in complex metric space,with some related control functions described the rational expression of generalized contractive conditions,set up and proved on several common fixed point of two classes of mapping results.Our r esults extend and extend the research results of Azam et al.,in order to verify the au thenticity of our results,and distinguish them from the existing results,and give some illustrative examples.In Chapter 4,we give a new fuzzy metric space(Y,M,*).At the same time,we give the related definitions of the M-Cauchy series and p-Cauchy series of the co mpression map in(Y,M,*).We establish a new fuzzy compression map in the M-complete fuzzy metric space.By iterative,the uniqueness of the fixed point of fuzzy compression mapping in(Y,M,*)is proved and its feasibility is verified.