Cone Metric Space And Fixed Point Theorems Of Multi-valued Mapping On Cones

Fixed point theorems of multi-valued mapping has important applications in Game Theorem, Mathematical Economics, Optimization Theory, Cybernetics and so on. In this paper, we considered of the equivalence of cone metric spaces and metric spaces, and fixed point theorems of multi-valued decreasing operators on cones.. The full text is divided into four chapters:Chapter I, Introduction: This chapter is mainly introduces the prior knowledge and the research situation in our country and abroad.Chapter II, the equivalence of cone metric spaces and metric space:through definition (?)on cone metic spaces( X, d). Proofed it is a metric on X . and proofed the equivalence of complete cone metric spaces and complete metric spaces. The priciple of Contraction Mapping in Banach Space is employed to proof the fixed point theorems on cone metric spaces , in essence, is a fixed point theorems on metric spaces.Chapter III, Fixed point theorems of multi-valuec decreasing operators on cones: In the paper, on one hand, we tras the multi-valued operator problem into single-valued operator problem. Through Ax = supTx, then we would proof the single-valued operator A which suit to the conditions of the convex and decreasing has fixed point with monotonous and iteration method from the condition of sup Tx∈Tx, thus we could proof the existence of the multi-valued opertor T . on the other hand, we give the proof of the existence of the multi-valued decreasing operator which satisfy two different order-contractive conditions, with sequence method.Chapter IV, the development and Dutiook of the paper.