A gap in the paper "A note on cone metric fixed point theory and its   equivalence" [Nonlinear Anal. 72(5), (2010), 2259-2261]
  There is a gap in Theorem 2.2 of the paper of Du (\cite{D_2010}). In this paper, we shall state the gap and repair it. 
Thabet Abdeljawad, Erdal Karap{\i}nar
math.FA