Study On Common Fixed Points And Coupled Fixed Points For Some Mappings In Generalized Metric Spaces

With the development of the theory and application of fixed point and public fixed point,the fixed point problem in metric spaces has attracted the attention of scholars in various fields and has been widely studied by a large number of mathematics scholars.In this paper,we discussed the existence and uniqueness of serious common fixed point problem and coupled fixed point problem in sev-eral generalized metric spaces and obtainsed some new results.It has important theoretical and application values.The full text consists of five chapters.In chapter 1,we introduce the historical background and research status of the fixed point area,as well as the main work and innovation of this article.In chapter 2,we introduce the not,ion of subcompatibility in G-metric s-paces.Under the condition that the mapings are subcompatible and reciprocally continuous,we prove several new common fixed point theorems.In chapter 3,we introduce a new class of twice power type contractive mapping in the complete S-metric spaces,and discuss the existence and uniqueness problem of the common fixed point for this type of contractive mapping,some new common fixed point theorems are obtained.In chapter 4,we introduce several new contractive conditions and prove a coupled coincidence point theorem and a coupled fixed point theorem for two mappings in Sb-metric spaces using the mixed g-monotone property.A common coupled fixed point theorem for three mappings also is got.And we give practical application examples to prove the validity of the results.In chapter 5,we prove a new common fixed point theorem for three pairs of weakly compatible mappings and several corollarys in Menger PGM-spaces,and provide illustrative examples in support of our new results.In this paper,we mainly study the common fixed point and coupled fixed point of the mapping in some generalized metric spaces that satisfy some new contractive conditions.We mainly introduce some new classes of mappings or new concepts to reduce some restrictions on spaces or mappings.And all the types of contractive mappings and new relative concepts are the first proposed and discussed in these spaces.So the results improve and develop the corresponding conclusions in these generalized metric spaces.