Some Common Fixed Points Theorems In Cone Metric Spaces

The problem of the existence of common fixed points for multivalued mappings, the problem of the existence of common fixed points for three mappings and the problem of the existence of common coupled fixed point are discussed in cone metric spaces. The paper contains five parts as following:In charter one, the background of fixed point theory, main contents that we will discuss and significance are introduced.In charter two, a new generalized contractive condition is introduced in met-ric space. By the condition and without the normality of the cone, the existence of common fixed points of multivalued mappings satisfying generalized contractive conditions in cone metric spaces is proved. These results extend some of the most general common fixed point theorems for two multivalued maps in cone metric s-paces.In charter three, a new multivalued S-T-sequence and some new generalized contractive conditions are introduced. By the conditions the existence of common fixed points of two multivalued mappings and a self-mapping satisfying generalized contractive conditions in normal cone metric spaces is proved. These results extend some of the most general common fixed point theorems for two multivalued maps in cone metric spaces.In charter four, a new generalized contractive condition is introduced in cone metric space. By the condition, the existence of common fixed points of three map-pings satisfying generalized contractive conditions in cone metric spaces is proved. These results extend some of the most general common fixed point theorems for two mappings in cone metric spaces.In charter five, a new generalized contractive condition is introduced in cone metric space. By the condition, the existence of common coupled coincidence point of the mappings F,G:X×Xâ†'X and f:Xâ†'X in cone metric spaces is proved. Moreover, by some condition the existence and uniqueness of common coupled fixed point of the mappings in cone metric spaces is proved. These results generalize some of the most general results in cone metric spaces.