Research On Common Fixed Point Problems In Probabilistic Metric Spaces

In probabilistic metric spaces, the distance between two elements is measured by a distribution function and an ordinary metric space can be viewed as a special case of a probabilistic metric space. Consequently, the research of nonlinear operators in PM-spaces is great significant. In this thesis, some nonlinear problems in PM- spaces are studied. It is divided into the following four sections.In Chapter one, the backgrounds and current situation of operator theory in PMspaces are introduced and the preliminaries of PM-spaces are given. The main job is also simply given.In Chapter two, the new concepts of multidimensional Menger probabilistic metric spaces and the corresponding t- norms are given, and the definition of n-tupled common fixed point and compatibility of the pair of mappings XXTn:?and :XXA ? are introduced. Then, based on the properties of generalized compatibility of mappings and generalized t- norms, the n-tupled common fixed point problems for hybrid probabilistic with a gauge function ? are discussed, and some new results are obtained.In Chapter three, the concept of a symmetric generalized probabilistic metric spaces is introduced, and without the compatibility and continuity of the mappings,the existence and uniqueness of the common fixed point of the mappings in such spaces are investigated, and some new fixed point theorems are established.In Chapter four, utilizing iterative methods, some existence problems on attractors for binary mappings in Menger probabilistic spaces are studied, and some new yet interesting conclusions are obtained, which generalize and extend the corresponding results in previous literature.