Mann and Ishikawa iterations with errors for asymptotically nonexpansive mappings

Authors
Citation
Zy. Huang, Mann and Ishikawa iterations with errors for asymptotically nonexpansive mappings, COMPUT MATH, 37(3), 1999, pp. 1-7
Citations number
9
Categorie Soggetti
Computer Science & Engineering
Journal title
COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN journal
08981221 → ACNP
Volume
37
Issue
3
Year of publication
1999
Pages
1 - 7
Database
ISI
SICI code
0898-1221(199902)37:3<1:MAIIWE>2.0.ZU;2-4
Abstract
In a recent paper, Rhoades [1] presented some generalizations of Schu [2] o n the convergence of the Mann and Ishikawa iterations of asymptotically non expansive mappings in uniformly convex Banach spaces. We continue the study on the Ishikawa land Mann) iteration process with errors and prove that if X is a uniformly convex Banach space, empty set not equal E subset of X cl osed bounded and convex, and T: E --> E is an asymptotically nonexpansive m apping, then the Ishikawa land Mann) iteration process with errors converge s strongly to some fixed point of T. (C) 1999 Elsevier Science Ltd. All rig hts reserved.