| Abstract: | In this paper, several weak and strong convergence theorems are established for a modified Noor iterative scheme with errors for three asymptotically nonexpansive mappings in Banach spaces. Mann-type, Ishikawa-type, and Noor-type iterations are covered by the new iteration scheme. Our results extend and improve the recently announced ones [B.L. Xu, M.A. Noor, Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 267 (2002) 444-453; Y.J. Cho, H. Zhou, G. Guo, Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings, Comput. Math. Appl. 47 (2004) 707-717] and many others. |
