Fixed points for mixed monotone multivalued operators in Banach spaces with applications

In this paper, the existence and iterative approximation of fixed points for a class of systems of mixed monotone multivalued operator are discussed. We present some new fixed point theorems of mixed monotone operators and increasing operators which need not be continuous or satisfy a compactness condition. We also give some applications to differential inclusions with discontinuous right hand side in Banach spaces and to Hammerstein integral inclusions on RN. © 2007 Elsevier Inc. All rights reserved