Fixed points of contractive type multivalued mappings (Q1088190)

Let X be a complete (resp. compact) Hausdorff uniform space whose uniformity is generated by a family of pseudometrics \(\{d_ i:\) \(i\in I\}\), and let \(2^ X\) be its hyperspace equipped with the Hausdorff uniformity induced by \(\{d_ i:\) \(i\in I\}\). By considering a pair \((F_ n,G_ n)\), \(n=1,2,..\). of multivalued mappings of X into \(2^ X\), we prove several common fixed point theorems in complete and compact uniform spaces. The pair \((F_ n,G_ n)\), \(n=1,2,..\). of multivalued mappings satisfies a contractive condition of very general nature.