Weak and strong convergence theorems for fixed points of asymptotically nonexpensive mappings

✍ Scribed by M.O. Osilike; S.C. Aniagbosor

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 822 KB
• Volume: 32
• Category: Article
• ISSN: 0895-7177
• DOI: 10.1016/s0895-7177(00)00199-0

✦ Synopsis

E be a uniformly convex Banach space, K a nonempty closed convex subset of E and T : K -K an asymptotically nonexpansive mapping with a nonempty fixed-point set. Weak and strong convergence theorems for the iterative approximation of fixed points of T are proved. Our results show that the boundedness requirement imposed on the subset K in recent, results of Huang [I], Rhoades [2], and Schu [3,4] can be dropped. Furthermore, our results extend these results to more satisfactory modified Mann and Ishikawa iteration methods with errors in the sense of Xu [5].