- Research Article
- Open Access
Strong Convergence to Common Fixed Points of a Finite Family of Nonexpansive Mappings
Journal of Inequalities and Applications volume 2007, Article number: 037513 (2007)
We suggest and analyze an iterative algorithm for a finite family of nonexpansive mappings. Further, we prove that the proposed iterative algorithm converges strongly to a common fixed point of.
Atsushiba S, Takahashi W: Strong convergence theorems for a finite family of nonexpansive mappings and applications. Indian Journal of Mathematics 1999,41(3):435–453.
Bauschke HH: The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space. Journal of Mathematical Analysis and Applications 1996,202(1):150–159. 10.1006/jmaa.1996.0308
Lions P-L: Approximation de points fixes de contractions. Comptes Rendus de l'Académie des Sciences. Séries A et B 1977,284(21):A1357-A1359.
Shimizu T, Takahashi W: Strong convergence to common fixed points of families of nonexpansive mappings. Journal of Mathematical Analysis and Applications 1997,211(1):71–83. 10.1006/jmaa.1997.5398
Takahashi W, Tamura T, Toyoda M: Approximation of common fixed points of a family of finite nonexpansive mappings in Banach spaces. Scientiae Mathematicae Japonicae 2002,56(3):475–480.
Zeng LC, Cubiotti P, Yao J-C: Approximation of common fixed points of families of nonexpansive mappings. to appear in Taiwanese Journal of Mathematics to appear in Taiwanese Journal of Mathematics
Wittmann R: Approximation of fixed points of nonexpansive mappings. Archiv der Mathematik 1992,58(5):486–491. 10.1007/BF01190119
Halpern B: Fixed points of nonexpanding maps. Bulletin of the American Mathematical Society 1967, 73: 957–961. 10.1090/S0002-9904-1967-11864-0
Kimura Y, Takahashi W, Toyoda M: Convergence to common fixed points of a finite family of nonexpansive mappings. Archiv der Mathematik 2005,84(4):350–363. 10.1007/s00013-004-1175-z
Xu H-K: Another control condition in an iterative method for nonexpansive mappings. Bulletin of the Australian Mathematical Society 2002,65(1):109–113. 10.1017/S0004972700020116
Bruck RE Jr.: Properties of fixed-point sets of nonexpansive mappings in Banach spaces. Transactions of the American Mathematical Society 1973, 179: 251–262.
Suzuki T: Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals. Journal of Mathematical Analysis and Applications 2005,305(1):227–239. 10.1016/j.jmaa.2004.11.017
Xu H-K: Viscosity approximation methods for nonexpansive mappings. Journal of Mathematical Analysis and Applications 2004,298(1):279–291. 10.1016/j.jmaa.2004.04.059
Takahashi W, Ueda Y: On Reich's strong convergence theorems for resolvents of accretive operators. Journal of Mathematical Analysis and Applications 1984,104(2):546–553. 10.1016/0022-247X(84)90019-2
About this article
Cite this article
Liou, YC., Yao, Y. & Kimura, K. Strong Convergence to Common Fixed Points of a Finite Family of Nonexpansive Mappings. J Inequal Appl 2007, 037513 (2007). https://doi.org/10.1155/2007/37513
- Iterative Algorithm
- Nonexpansive Mapping
- Strong Convergence
- Finite Family