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We prove that if a continuous surjective map f on a compactmetric space X has the average shadowing property, then everypoint x is chain recurrent.We also show that if a homeomorphism f has more than two fixed points on S^1,then f does not satisfy the average shadowing property.Moreover, we construct a homeomorphism on a circle which satisfies the shadowing propertybut not the average shadowing property.This shows that the converse of the theorem 1.1 in [6] is not true.