Several Types Of Fixed Point Theorems For Contractive Mappings In Cone Metric Spaces

Fixed point theorems in metric spaces is an important part of Nonlinear Functional Analysis, since cone metric space has defined, fixed point theorems in cone metric spaces has become an active research topic in recent years. The research focus has shifted from the normal cone to non-normal, and extended the classic Banach contraction to nonlinear, generalized and weaker contraction. Some fixed point theorems also emerge in an endless stream. This paper mainly discusses the several types of fixed point theorems for contractive mappings in cone metric spaces, The full text is divided into four parts, Which reads as follows:The first chapter is an introduction, Introduces the current research status of fixed point theory in cone metric space and the background knowledge needed in this paper, and the main work of this article and meaning.The second chapter, we cites the concept of weakly compatible mappings in cone metric spaces, and proposed two fixed point theorems for four self-mappings which satisfy a generalized contractive condition, The contractive condition Suitable for a set of mappings. Enrich and extend the common fixed point theory of multiple mappings.The third chapter, firstly we discussed common coupled coincidence point theorems satisfying a generalized contractive condition defined by φ-maps on cone metric spaces. And then we prove common coupled fixed point theorems involving two pairs of w-compatible mappings. Extend the common coupled coincidence point theorems.In the fourth chapter we give the main conclusions of the previous chapters corresponding to the relevant application examples, illustrates the correctness and usefulness of the conclusions.