Remarks on fixed point theorem of multivalued nonexpansive mapping in Banach lattices
Jingxin Zhang · Journal of Natural Science of Heilongjiang University · 2011
In Banach spaces,the(DL) condition implies that multivalued nonexpansive mapping defining on compact sets has fixed point.Hence,a possible approach to find the fixed point of multivalued nonexpansive mapping is to look for geometric conditions in a Banach space which imply(DL) condition.It is proven that a weakly orthogonal Banach lattice with e0,m(X)1 satisfies the(DL) condition,thus has multivalued fixed point property.Simultaneously,it is obtained that nonself multivalued nonexpansive mapping satisfying Inward condition has fixed point.These results extend the original paper′s results.