Research On Some Fixed Points Problems In Probabilistic Metric Spaces

Through studing, we can find that the distance between two elements in probabilistic metric spaces is measured by a distribution function and an ordinary metric space can be viewed as a special case of a probabilistic metric space. Recently, some people are intrested in the research on some fixed points problems in and out of the broad. The fixed points problems can be considered as an important part of probabilistic analysis, which is connected with some parts of mathematics, especially play an imported role in the existence and uniqueness of some equations. Consequently, probabilistic metric spaces, as an important generalization of metric space, the theory of fixed points in PM-spaces is also of great significance.In this thesis, some new fixed points problems and application in PM-spaces are studied. It is divided into the following three sections.In chapter one, the backgrounds and current situation of fixed points theory in PM-spaces are introduced and the preliminaries which will be needed in this paper are given.In chapter two, the notion of converse commuting mappings, single-valued occasionally weakly compatible mappings and multi-valued occasionally weakly compatible mappings are introduced in M-PM space. And we study the existence and uniqueness of common fixed point theorems for the mappings satisfying the above conditions. In the meantime, we apply these results to Fuzzy metric spaces, improve and generalize some main results.In chapter three, the concepts of compatible mappings and compatible mappings of type(A) in Menger probabilistic 2-metic spaces are introduced. And we study the existence and uniqueness of common fixed point theorems for compatible mappings and compatible mappings of type(A) underΦ-contractive conditions. Meanwhile, we improve and generalize some important conclusions and give some applications in fuzzy metric spaces.