The modified Noor iterations with errors for non-Lipschitzian mappings in Banach spaces - Nammanee K. (2014)
In this paper, weak and strong convergence theorems are established for the modified Noor iterations with errors for asymptotically nonexpansive mappings in the intermediate sense in a uniformly convex Banach space. Mann-type and Ishikawa-type iterations are included by the modified Noor iterations with errors. The results obtained in this paper extend and improve the recent ones announced by Schu [J. Schu, Iterative construction of fixed points of asymptotically nonexpansive mappings, J. Math. Anal. Appl. 158 (1991) 407-413; J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc. 43 (1991) 153-159], Xu and Noor [B.L. Xu, M.A. Noor, Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 267 (2002) 444-453], Cho et al. [Y.J. Cho, H.Y. 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], Suantai [S. Suantai, Weak and strong convergence criteria of Noor Iterations for asymptotically nonexpansive mappings, J. Math. Anal. Appl. 311 (2005) 506-517], Nammanee et al. [K. Nammanee, M.A. Noor, S. Suantai, Convergence criteria of modified Noor iterations with errors for asymptotically nonexpansive mappings, J. Math. Anal. Appl. 314 (2006) 320-334], and many others. © 2006 Elsevier Inc. All rights reserved.