Further Research About Common Fixed Point And Coupled Fixed Point Problems

In recent years, fixed point theorems and it’s application has achieved great development, many authors obtained important results. Base on the study of the Predecessors, the content of this paper was more widely and the results were more applicable by changing spaces !structuring new contraction conditions and the type of mappings ! adding the number of mappings. The mainly study of this thesis was about the existence and uniqueness of fixed point problem, such as compatible mappings of type(A)!converse commuting mappings!contraction mapping for twice power type on generalized metric space. In addition§we discussed the common tripled fixed point problem on generalized metric space and common fixed point theorem for converse commuting self-mappings on partial metric space. Our results have improved and developed the fixed point theory on generalized metric space and partial metric space, such that it was more generally,innovative and practical.This paper is divided into four chapters.In chapter 1, we introduced the research background and current situation analysis of the fixed point theory and the common tripled fixed point theory on generalized metric space and partial metric space.In chapter 2, our mainly study contents were all discussed on generalized metric space,and it includes the following three aspects:(1)Use the concept of weakly compatible mappings of type(A) to discuss a new common fixed point problem for six self-mappings in G-metric spaces, and we provided an example to support our new result;(2)Use the concept of converse commuting mappings to discuss common fixed point problem on partial metric spaces without completeness and Continuity, and an example was proved to support our new result;(3)Use the concept of common(E.A) property and weakly compatible mappings to discuss common fixed point problem for a class of twice power type contractive mappings in the framework of a generalized metric space, and our results did not rely on any commuting or continuity condition of mappings. We also stated some examples to illustrate our new results in the framework of symmetric and nonsymmetric generalized metric spaces.In chapter 3, we obtained some common tripled fixed point theorems for four mappings in generalized metric spaces satisfying some contractive conditions.Also,relevant examples have been cited to illustrate the e?ectiveness of our results.Meanwhile, we demonstrated the existence and uniqueness of solution of system of nonlinear integral equations by applying the above result.In chapter 4, we discussed the existence and uniqueness of common fixed point theorem for converse commuting self-mappings on partial metric spaces without completeness and continuity, and obtained some new results, an example was proved to support our new result.