Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings

In this paper, weak and strong convergence theorems are established for a three-step iterative scheme for asymptotically nonexpansive mappings in Banach spaces. Mann-type and Ishikawa -type iterations are included by the new iterative scheme. The results obtained in this paper extend and improve the recent ones announced by Xu and Noor, Glowinski and Le Tallec, Noor, Ishikawa, and many others.