The Fixed Point Theorem And Applied Research Of A Number Of Nonlinear Operators

We all known the fixed point theorem and common fixed point theorem in metric spaces have been studied by serious mathematical author.In this paper,we will further study this problem.Our purpose is to extend some known results in metric space to multiplicative metric space,multiplicative b-metric space and multiplicative b-metric-like space.The problem of common fixed point theorem and common coupled fixed point theorem are mainly studied in those spaces.Meantime,we also provide some examples to support our new results.In chapter 1,we introduced the research background and foreign research in our field.In chapter 2,in the framework of a multiplicative metric spaces,we in-troduce concept of(?)-weakly commuting mappings,we prove some new fixed point theorem for four mappings using compatible mappings and(?)-weakly commuting mappings.The results extend and improve some well-known comparable results in multiplicative metric space.In chapter 3,by using the concept of a complete multiplicative b-metric spaces,we prove some new fixed point theorem for gener-alized F-Suzuki-contraction mappings.A practical example is given to illustrate the effectiveness of the new results.In chapter 4,in multiplicative metric space,by using the concept of ?*-compatible mappings,we establish some new common coupled fixed point theorems for two mappings satisfying 0-type contractive con-dition.It is worth noting that we not only gives practical examples to support our new results,but also successfully applied the new results to solve the problems of the existence and uniqueness of common solutions of a class of nonlinear integral equations.The result of this chapter is new,so far there is no discussion of these issues;In chapter 5,we will establish a new coupled coincidence point and coupled fixed point theorem in multiplicative b-metric-like spaces.At the same time,we also will provide a example to support our new results.