Research On Some Nonlinear Problems In Partial Metric Spaces

In1994, Matthews proposed the concept of partial metric space on the basis ofmetric spaces, and studied the Banach contraction mapping principle in partialmetric space. The partial metric space generalizes the general metric space, theresearch of the problem of nonlinear in partial metric space contributes importantacademic value and scientific significance to the enrichment and development thetheory of nonlinear analysis. This paper mainly studied some fixed point problems ofseveral kinds of mapping in partial metric spaces. There are three chapters in thisthesis.In chapter one, the historical backgrounds and current situation of partial metricspace theory and application are introduced and some related concepts of partialmetric spaces are given.In chapter two, the generalized,L-weak contraction and generalized (, L)-weak contraction mappings are defined and some new fixed point theorems for thesetype contraction mappings are proved by iterative approach in partial metric spaces.In chapter three, some new expanding conditions of mappings are proposed inthe partial metric spaces and a new fixed point theorem of expanding mappings isgiven. These results generalize the existing related conclusions.