Existence and uniqueness of fixed points for mixed monotone multivalued operators in Banach spaces

In this paper, the existence and approximation of fixed points for two classes of systems of mixed monotone (downward and upward) multivalued operators are discussed. We present some new fixed point theorems of mixed monotone(downward and upward)operators which need not be continuous and compact. We also indicate the condition to ensure the uniqueness of the fixed point. At last we get some applications of our theorems.