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Strong convergence to common fixed points of nonexpansive mappings without commutativity assumption
Fixed Point Theory and Applications volume 2006, Article number: 89470 (2006)
Abstract
We introduce an iteration scheme for nonexpansive mappings in a Hilbert space and prove that the iteration converges strongly to common fixed points of the mappings without commutativity assumption.
References
Baillon J-B: Un théorème de type ergodique pour les contractions non linéaires dans un espace de Hilbert. Comptes Rendus de l'Académie des Sciences de Paris, Série. A-B 1975,280(22):A1511-A1514.
Brézis H, Browder FE: Nonlinear ergodic theorems. Bulletin of the American Mathematical Society 1976,82(6):959–961. 10.1090/S0002-9904-1976-14233-4
Halpern B: Fixed points of nonexpanding maps. Bulletin of the American Mathematical Society 1967, 73: 957–961. 10.1090/S0002-9904-1967-11864-0
Jung JS: Viscosity approximation methods for a family of finite nonexpansive mappings in Banach spaces. Nonlinear Analysis 2006,64(11):2536–2552. 10.1016/j.na.2005.08.032
Maingé P-E: Viscosity methods for zeroes of accretive operators. Journal of Approximation Theory 2006,140(2):127–140. 10.1016/j.jat.2005.11.017
Opial Z: Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bulletin of the American Mathematical Society 1967, 73: 591–597. 10.1090/S0002-9904-1967-11761-0
Reich S: Some problems and results in fixed point theory. In Topological Methods in Nonlinear Functional Analysis (Toronto, Ont., 1982), Contemp. Math.. Volume 21. American Mathematical Society, Rhode Island; 1983:179–187.
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
Wittmann R: Approximation of fixed points of nonexpansive mappings. Archiv der Mathematik 1992,58(5):486–491. 10.1007/BF01190119
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
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Yao, Y., Chen, R. & Zhou, H. Strong convergence to common fixed points of nonexpansive mappings without commutativity assumption. Fixed Point Theory Appl 2006, 89470 (2006). https://doi.org/10.1155/FPTA/2006/89470
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DOI: https://doi.org/10.1155/FPTA/2006/89470