A reconsideration on equivalency of convergence between iterations for uniformly -Lipschitzian operators

This paper is to illustrate that the conditions and proofs of three theorems of S.S. Chang, Y.J. Cho and J.K. Kim [The equivalence between the convergence of modified Picard, modified Mann and modified Ishikawa iterations, Math. Comput. Modelling 37 (2003) 985–991] concerning the equivalence between the convergence of modified Picard, modified Mann and modified Ishikawa iterations for uniformly Lipschitzian operators in arbitrary Banach spaces are incorrect.