Fixed point theory of multimaps in abstract convex uniform spaces

摘要

This is to establish fixed point theorems for multimaps in abstract convex uniform spaces.Our new results generalize corresponding ones in topological vector spaces (t.v.s.), convexspaces due to Lassonde, C-spaces due to Horvath, and G-convex spaces due to Park.We show that fixed point theorems on multimaps of the Fan-Browder type, multimapshaving ranges of the Zima-Hadii( type, and multimaps whose ranges are 1-sets or Kleeapproximable sets can be established in abstract convex spaces or KKM spaces.