Fixed point theory of multimaps in abstract convex uniform spaces Original Research Article

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.), convex spaces due to Lassonde, CC-spaces due to Horvath, and GG-convex spaces due to Park. We show that fixed point theorems on multimaps of the Fan–Browder type, multimaps having ranges of the Zima–Hadžić type, and multimaps whose ranges are ΦΦ-sets or Klee approximable sets can be established in abstract convex spaces or KKM spaces.