Research On Several Non-linear Problems In Partial Metric Spaces And Cone Metric Spaces

In the process of nonlinear analysis research,the fixed point problems have been widely concerned.In recent years,people pay great attention on best proximity point problem.Some scholors achieved some good results. It is applied to many different fields. In this paper,respectively, research have been done about best proximity point and common best proximity point on partial metric spaces and common fixed point s on cone metric spaces.There are three chapters in this thesis.Chapter 1 The exordium is a review of the historical background of nonlinear functional analysis and current research situation and gives some basic concepts in nonlinear analysis.Chapter 2 Generalized proximal contraction, weak proximal contraction and weakly proximal dominate are proposed in partial metric spaces. Furthermore, we get the best proximity point for generalized and weak proximal contraction and common best proximity point for a pair of non-self mappings, one of which weakly dominates the other proximally in partial metric spaces.Chapter 3 This chapter mainly discusses a common fixed point theorem for a family of non-self mappings on cone metric spaces. Simultaneously, we give an example to illustrate the validity of our main results. And these results generalize the related results.