2007
DOI: 10.1155/2007/64874
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A New Iterative Algorithm for Approximating Common Fixed Points for Asymptotically Nonexpansive Mappings

Abstract: Suppose that K is a nonempty closed convex subset of a real uniformly convex and smooth Banach space E with P as a sunny nonexpansive retraction. Let T 1 ,T 2 : K → E be two weakly inward and asymptotically nonexpansive mappings with respect to P with sequences {K n }, {l n } ⊂ [1,∞), lim n→∞ k n = 1, lim n→∞ l n = 1, F(T 1) ∩ F(T 2) = {x ∈ K : T 1 x = T 2 x = x} = ∅, respectively. Suppose that {x n } is a sequence in K generated iteratively by x 1 ∈ K, x n+1 = α n x n + β n (PT 1) n x n + γ n (PT 2) n x n , f… Show more

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Cited by 27 publications
(27 citation statements)
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“…In this paper, a new one-step iterative scheme with error for approximating common fixed points of asymptotically quasi-nonexpansive type nonself-mappings in Banach space is defined. The results obtained in this paper extend and improve the recent ones, announced by H. Y. Zhou, Y. J. Cho, and S. M. Kang [Zhou et al,(2007), namely, A new iterative algorithm for approximating common fixed points for asymptotically nonexpansive mappings, published to Fixed Point Theory and Applications 2007 : 1-9], and many others. …”
supporting
confidence: 82%
See 3 more Smart Citations
“…In this paper, a new one-step iterative scheme with error for approximating common fixed points of asymptotically quasi-nonexpansive type nonself-mappings in Banach space is defined. The results obtained in this paper extend and improve the recent ones, announced by H. Y. Zhou, Y. J. Cho, and S. M. Kang [Zhou et al,(2007), namely, A new iterative algorithm for approximating common fixed points for asymptotically nonexpansive mappings, published to Fixed Point Theory and Applications 2007 : 1-9], and many others. …”
supporting
confidence: 82%
“…Recently, H. Y. Zhou, Y. J. Cho, and S. M. Kang [8] gave a new iterative scheme(5) for approximating common fixed point of two asymptotically nonexpansive nonself-mappings with respect to P and proving some strong and weak convergence theorems for such mappings in uniformly convex Banach spaces.…”
Section: The Mapping T Is Called Uniformly L-lipschitzian If There Exmentioning
confidence: 99%
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“…Further, the set F(T) is closed and convex. Since 1972, a host of authors have studied the weak and strong convergence problems of the iterative algorithms for such a class of mappings (see, e.g., [4][5][6] and the references therein).…”
Section: Introduction and Preliminarymentioning
confidence: 99%