... zi∈ X, i 1, 2, ,n.Proof. The proofs of 1 and 2 are easy and left to the reader. In order to prove 3,letx, y, z1, ,znbe any points in X. Using the triangle inequality satisfied by ... 3.9Since limn →∞LipTn0, then {Tnx} is a Cauchy sequence. Hence {Tnx} converges to somepoint ωx since X is complete. The remaining part of the proof follows the same as in theprevious ... Rzepecki in 2. After carefully defining convergence and completeness in cone metric spaces, theauthors proved some fixed point theorems of contractive mappings. Recently, more fixedpoint results in...