Weak and strong convergence of the Ishikawa iteration process with errors for two asymptotically nonexpansive mappings. (English) Zbl 1107.65046

Authors’ summary: We prove the weak and strong convergence of the Ishikawa iterative scheme with errors to a common fixed point for two asymptotically nonexpansive mappings in a uniformly convex Banach space under a condition weaker than compactness. Our theorems improve and generalize recent known results in the literature.


65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
Full Text: DOI


[1] Goebal, K.; Kirk, W. A., A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35, 171-174 (1972) · Zbl 0256.47045
[2] Górnicki, J., Weak convergence theorems for asymptotically nonexpansive mappings in uniformly convex Banach spaces, Comment. Math. Univ. Carolin., 30, 249-252 (1989) · Zbl 0686.47045
[3] Khan, S. H.; Fukhar-ud-din, Hafiz, Weak and strong convergence of a scheme with errors for two nonexpansive mappings, Nonlinear Analysis, 61, 1295-1301 (2005) · Zbl 1086.47050
[4] Opial, Z., Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73, 591-597 (1967) · Zbl 0179.19902
[5] Schu, J., Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Aust. Math. Soc., 43, 153-159 (1991) · Zbl 0709.47051
[6] Takahashi, W.; Tamura, T., Convergence theorems for a pair of nonexpansive mappings, J. Convex Analysis, 5, 1, 45-48 (1998) · Zbl 0916.47042
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.