The Common Fixed Point Of Multivalued Operators In In Metric Space

In this paper, we first give some definitions and theories in the metric space. According to these definitions and theories, we discuss the existence of the common fixed point about the multivalued operators. Our results are the extension and improvement of the corresponding single-valued operator results. In particular, some results in which also gives the operator more than the value of the uniqueness of fixed points, these results are new. For some results, we give a corresponding example of the effectiveness and practical of the results.First chapter is introduction, mainly introduce some results of former researcher and their methods and mathematical tools which deal with these problems, and we enumerate the problems of which will be solved in our paper.In the second chapter, we mainly give some definitions and theories, containing the basic concepts of the cone metric space. Furthermore, we also define the concept of the integral operator in cone metric space and give some basic knowledge of the multi-valued operators. For example, the concept of the Hausdorff metric. Not only are the problem of the multi-valued operators more difficult than the single-valued operators, but also some problems can not resolve. By introducing the notion of order, we get the conclusion of the existence of common fixed point under the assumption of the partial order. We list some conclusions that have been done by professors. They gave the theories of the single-valued operators and obtained the satisfied conclusions. On the basic of the original conclusions, we modified and promoted the conditions of the original conclusions and got the conclusion that we wanted. Some of the contractive conditions are not the general contractive conditions. For example the contractive conditions that are constituted by the cone integrable function. They got the common fixed point of the single-valued operators. It is the aim that we get the existence and uniqueness of the common fixed point about the multi-valued operators. The uniqueness of the common fixed point is a very good conclusion and we did not add the additional contractive conditions.In the third chapter, we mainly research the common fixed point of the general contractive multi-valued operators in the complete cone metric space. Essentially, we construct the common fixed point of multi-valued operators by the previous result in the single-valued operators and add some qualifiers. So the result is new to the single-valued operators also. Our result not only have the meaning of the theory but also have the practical value. Last we cite the example .In the Forth chapter, we got the common fixed point of the multi-valued operators in the complete cone metric space. The contractive condition is constructed by the cone integaral function. Because we consider the common fixed point of multi-valued operators. In this chapter, we not only defined the strong small cone in the cone metric space, but also gave the concept of the Hausdorff metric about the strong small cone. By introducing the notion of order, we get the conclusion of the existence of common fixed point under the assumption of the partial order, also, the uniqueness of common fixed point under the assumption of total order.In the end of the paper we combine with our thoughts to get the expectation of our research realm, while point out the amelioration of our theories.