The equivalence between Mann–Ishikawa iterations and multistep iteration

Abstract We show that the convergence of Mann, Ishikawa iterations are equivalent to the convergence of a multistep iteration, for various classes of operators.

[1]  Klaus Deimling,et al.  Zeros of accretive operators , 1974 .

[2]  C. Morales,et al.  Convergence of paths for pseudo-contractive mappings in Banach spaces , 2000 .

[3]  Stefan M. Soltuz,et al.  ON THE EQUIVALENCE OF MANN AND ISHIKAWA ITERATION METHODS , 2003 .

[4]  B. Rhoades,et al.  The equivalence of Mann iteration and Ishikawa iteration for a Lipschitzian $ \psi $- uniformly pseudocontractive and $ \psi $- uniformly accretive maps , 2004 .

[5]  C. E. Chidume,et al.  An example on the Mann iteration method for Lipschitz pseudocontractions , 2001 .

[6]  Billy E. Rhoades,et al.  The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitzian operators , 2003 .

[7]  M. Noor.  New approximation schemes for general variational inequalities , 2000 .

[8]  C. H. Morales.  Convergence of paths for pseudocontractive mappings in Banach spaces , 2000 .

[9]  S. Ishikawa.  Fixed points by a new iteration method , 1974 .

[10]  Muhammad Aslam Noor,et al.  Three-step iterations for nonlinear accretive operator equations , 2002 .

[11]  K. Deimling.  Nonlinear functional analysis , 1985 .

[12]  Ştefan M. Şoltuz,et al.  The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps , 2004 .

[13]  Xinlong Weng,et al.  Fixed point iteration for local strictly pseudo-contractive mapping , 1991 .

[14]  W. R. Mann,et al.  Mean value methods in iteration , 1953 .

[15]  Ştefan M. Şoltuz,et al.  The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically pseudocontractive map , 2003 .