The Problems On Common Fixed Point For Nonlinear Mapping In Generalized Metric Spaces

The fixed point problem in metric spaces have been studied by serious math-ematical author.The study of this paper involves fixed point theorems for a more general b-metric space and a patrial b-metric space.Especially,we discussed the existence and uniqueness of serious coupled fixed point problem in ordered patrial b-metric space and got many new results.These results improved and generalized the common fixed point theorems.Therefore,the study is of great significance and practical value.In chapter 1,we introduced the research background and foreign research in our field.In chapter 2,we introduced compatible mappings of type(P)in b-metric spaces,and discussed a new third power type contractive condition.By using the compatible mappings of type(P)and weakly compatible mappings,we proved a new common fixed point theorem.Meanwhile,the existing conclusions in metric spaces will be generalized and improved.In chapter 3,by using the concept of weakly compatible maps,we proved some new common fixed point theorem in b-metric spaces.Meanwhile,the existing conclusions in metric spaces were generalized and improved.In chapter 4,we introduced some new coupled fixed point theorems in ordered partial b-metric spaces in this paper.Meantime,an example was given to support the value of our results.Our results improved and extended the common coupled fixed point theorems from b-metric space and partial metric space to ordered partial b-metric space.In chapter 5,without the condition of mixed monotone property,we discussed the problem of common coupled fixed point for two functions of two variables in partial b-metric spaces,and got some new common coupled fixed point theorems.In addition,an example was given to support the value of our results.