## 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.

### MSC:

 65J15 Numerical solutions to equations with nonlinear operators 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc.
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### References:

 [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
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