The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous φ‐strongly accretive operators in uniformly smooth Banach spaces
Zeqing Liu, Li Wang, Jeong Sheok Ume, Shin Min Kang · International Journal of Mathematics and Mathematical Sciences · 2006
We investigate the equivalence between the convergences of the Mann iteration method and the Ishikawa iteration method with errors for demicontinuous φ‐strongly accretive operators in uniformly smooth Banach spaces. A related result deals with the equivalence of the Mann iteration method and the Ishikawa iteration method for φ‐pseudocontractive operators in nonempty closed convex subsets of uniformly smooth Banach spaces. The results presented in this paper extend and improve the corresponding results in the literature.