In this paper, we establish some fixed point theorems for a family of multivalued maps under mild
conditions. By using our fixed point theorems, we derive some maximal element theorems for a
particular family of multivalued maps, namely the Φ-condensing multivalued maps. As applications
of our results, we prove some general equilibrium existence theorems in the generalized abstract
economies with preference correspondences. Further applications of our results are also given to
minimax inequalities for a family of functions.
2003 Elsevier Inc. All rights reserved.
Journal of Mathematical Analysis and Applications,284(2):656-671