Fixed point theorems for Monch type maps in abstract convex uniform spaces

In this paper, first, we present new fixed point theorems for Monch type multimaps on abstract convex uniform spaces and, also, a fixed point theorem for Monch type multimaps in Hausdorff KKM L\G-spaces. Second, we show that Monch type multimaps in the ’better’ admissible class defined on an L\G-space have fixed point properties whenever their ranges are Klee approximable. Finally, we obtain fixed point theorems on $\mathfrak {KC}$ maps whose ranges are Φ-sets.