Common fixed points theorems for fuzzy mappings

Recently, Abu-Donia [Abu-Donia HM. Common fixed points theorems for fuzzy mappings in metric space under contraction condition. Chaos, Solitons & Fractals 2007;34:538–43] studied the Hausdorff metric between fuzzy subsets via its correspondence between the two classical sets and established two common fixed point theorems for two fuzzy mappings which are useful in geometric problems arising in high energy physics. However, the proofs of Abu-Donia’s main results are incorrect. The purpose of this paper is to present correct proofs of these results.