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Strong convergence to common fixed points of two asymptotically nonexpansive mappings. (English) Zbl 1203.47068
Kato, Mikio (ed.) et al., Proceedings of the 2nd international symposium on Banach and function spaces II (ISBFS 2006), Kitakyushu, Japan, September 14--17, 2006. Yokohama: Yokohama Publishers (ISBN 978-4-946552-29-8/hbk). 421-429 (2008).
Summary: In this paper, we establish a strong convergence theorem for finding a common fixed point of asymptotically nonexpansive mappings by using the hybrid method in a Hilbert space. Moreover, we also prove a strong convergence theorem for a common fixed point of two nonexpansive mappings. Our results extend and improve the recent ones announced by {\it T.-H.\thinspace Kim} and {\it H. K.\thinspace Xu} [Nonlinear Anal. Nonlinear Anal., Theory Methods Appl. 64, No. 5, 1140--1152 (2006; Zbl 1090.47059], {\it K. Nakajo} and {\it W. Takahashi} [J. Math. Anal. Appl. 279, No. 2, 372--379 (2003; Zbl 1035.47048)], and others. For the entire collection see [Zbl 1138.46001].

47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
47H10Fixed-point theorems for nonlinear operators on topological linear spaces