Common Coupled Fixed Point Theorems For Contractive Mappings Of Many Variables In Fuzzy Metric Spaces

In this paper,on the basis of fuzzy metric spaces and related theories of ?-contraction,we introduce the defination of coupled coincidence point of multiple mappings between any number of variables through the concept of ?-coincidence point.Then we prove the fixed point theorems of multiple mappings in partially ordered fuzzy metric spaces,This theorem is an extension of fixed point theorem in partially ordered fuzzy metric spaces from low dimension to high dimension.(1)In the first chapter,we introduce the background of fixed point theory,summarize the research status and achievements of fuzzy metric space and ?-contraction,which inspire the research ideas of this paper.(2)In the second chapter,we introduce the definition of fixed point classification of multiple mappings,the definition of fuzzy metric space,the fixed point theorem of ?-contraction in fuzzy metric space,and the definition of the multiple mappings relationship,which provides a theoretical basis for the further discussion of the common coupled fixed point theorem of multiple mappings of high dimension in fuzzy metric space under the condition of ?-contraction.(3)In the third chapter,we propose and prove the main conclusion of this paper,that is,the common coupled fixed point theorem for multivariable contractive mappings in fuzzy metric spaces,and generalize some existing conclusions based on this theorem.(4)Finally,the fourth chapter reviews and summarizes the work of this paper,and puts forward some thinking directions related to this problem.