On the equivalence of the convergence criteria between modified Mann-Ishikawa and multi-step iterations with errors for successively strongly pseudo-contractive operators
The authors prove the equivalence of the convergence between the modified Mann- Ishikawa and multi-step Noor iterations with errors for the successively strongly pseudo-contractive operators without Lipschitzian assumption. By extending to the more generalized multi-step iterations with errors, the results obtained in this paper generalize the results of \textit{B. E. Rhoades} and \textit{S. M. Soltuz} [Nonlinear Anal., Theory Methods Appl. 58A, No. 1--2, 219--228 (2004; Zbl 1064.47070); J. Math. Anal. Appl. 289, 266--278 (2004; Zbl 1053.47055)]. On the other hand, by providing the equivalence of convergence between all of these up-to-date iteration schemes, these results improve the corresponding results of all references in the bibliography.
scientific article; zbMATH DE number 5069180