## Strong convergence to common fixed points for countable families of asymptotically nonexpansive mappings and semigroups.(English)Zbl 1217.47132

The authors prove some strong convergence theorems for countable families of asymptotically nonexpansive mappings and semigroups in Hilbert spaces. Their results extend and improve some recently announced ones.

### MSC:

 47J25 Iterative procedures involving nonlinear operators 47H20 Semigroups of nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc.
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### References:

 [1] Mann, WR, Mean value methods in iteration, Proceedings of the American Mathematical Society, 4, 506-510, (1953) · Zbl 0050.11603 [2] Halpern, B, Fixed points of nonexpanding maps, Bulletin of the American Mathematical Society, 73, 957-961, (1967) · Zbl 0177.19101 [3] Nakajo, K; Takahashi, W, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, Journal of Mathematical Analysis and Applications, 279, 372-379, (2003) · Zbl 1035.47048 [4] Kim, T-H; Xu, H-K, Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Analysis: Theory, Methods & Applications, 64, 1140-1152, (2006) · Zbl 1090.47059 [5] Zegeye, H; Shahzad, N, Strong convergence theorems for a finite family of asymptotically nonexpansive mappings and semigroups, Nonlinear Analysis: Theory, Methods & Applications, 69, 4496-4503, (2008) · Zbl 1168.47056 [6] Su, Y; Qin, X, Strong convergence of monotone hybrid method for fixed point iteration processes, Journal of Systems Science & Complexity, 21, 474-482, (2008) · Zbl 1222.47120 [7] Takahashi, W; Takeuchi, Y; Kubota, R, Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces, Journal of Mathematical Analysis and Applications, 341, 276-286, (2008) · Zbl 1134.47052 [8] Su, Y; Qin, X, Strong convergence theorems for asymptotically nonexpansive mappings and asymptotically nonexpansive semigroups, 11, (2006) · Zbl 1143.47307 [9] Nakajo, K; Shimoji, K; Takahashi, W, Strong convergence to common fixed points of families of nonexpansive mappings in Banach spaces, Journal of Nonlinear and Convex Analysis, 8, 11-34, (2007) · Zbl 1125.49024 [10] Opial, Z, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bulletin of the American Mathematical Society, 73, 591-597, (1967) · Zbl 0179.19902 [11] Lin, P-K; Tan, K-K; Xu, HK, Demiclosedness principle and asymptotic behavior for asymptotically nonexpansive mappings, Nonlinear Analysis: Theory, Methods & Applications, 24, 929-946, (1995) · Zbl 0865.47040
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