Some Fixed Point Theorems In Cone B-metric Spaces

The fixed point theory in metric spaces is an important part of nonlinear function anal-ysis. Since Huang and Zhang [1] recently introduced the concept of cone metric space, replacing real number by ordered Banach space, the fixed point theorems in cone metric s-paces become the hot topic that people study in the recent years. In this paper, we mainly study the existence and uniqueness of fixed point theorems for some kinds of contractive mappings, such that contractive mapping, generalized quasi-contractive mapping, general-ized operator quasi-contractive mapping in cone b-metric spaces, with the condition that the cone is not assumed to be normal. Examples are given to distinguish these results from the known ones. This paper includes five chapters. Now we will describe them briefly one byChapter1, as an introduction, we recall the history and the current research status of the fixed point theorems in cone b-metric spaces, and also give a summary of this work.Chapter2, in this section, we give some common fixed point results for two weakly compatible self-mappings satisfying contractive condition or quasi-contractive condition in the case of a contractive constant λ∈(0,1/s) in cone6-metric spaces without the assump-tion of normality.Chapter3, in this section, we will present some fixed point results of generalized quasi-contractive mappings in the case of a constant κ∈(0,1/s) in cone b-metric spaces without the assumption of normality.Chapter4, we will present fixed point theorem of generalized operator quasi-contractive mapping in cone b-metric spaces without the assumption of normality, continuity.Finally, corresponding examples of the former chapters are given to support our new results.