Approximating common fixed points for a finite family of asymptotically nonexpansive mappings using iteration process with errors terms
Let X be a real Banach space and K a nonempty closed convex subset of X. Let T i: K → K (i = 1, 2,., m) be m asymptotically nonexpansive mappings with sequence { k n } ⊂ [ 1, ∞), ∑ n = 1 ∞ (k n - 1) < ∞, and F = ∩ i = 1 m F (T i) ≠ ∅, where F is the set of fixed points of T i. Suppose that { a i...
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| 主要な著者: | , |
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| フォーマット: | 論文 |
| 言語: | English |
| 出版事項: |
Hindawi Publishing Corporation
2013
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| オンライン･アクセス: | http://psasir.upm.edu.my/id/eprint/30280/1/30280.pdf http://psasir.upm.edu.my/id/eprint/30280/ http://www.hindawi.com/journals/aaa/2013/974317/ |
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| 要約: | Let X be a real Banach space and K a nonempty closed convex subset of X. Let T i: K → K (i = 1, 2,., m) be m asymptotically nonexpansive mappings with sequence { k n } ⊂ [ 1, ∞), ∑ n = 1 ∞ (k n - 1) < ∞, and F = ∩ i = 1 m F (T i) ≠ ∅, where F is the set of fixed points of T i. Suppose that { a i n } n = 1 ∞, { b i n } n = 1 ∞, i = 1,2,., m are appropriate sequences in [ 0,1 ] and { u i n } n = 1 ∞, i = 1,2,., m are bounded sequences in K such that ∑ n = 1 ∞ b i n < ∞ for i = 1,2,., m. We give { x n } defined by x 1 ∈ K, x n + 1 = (1 - a 1 n - b 1 n) y n + m - 2 + a 1 n T 1 n y n + m - 2 + b 1 n u 1 n, y n + m - 2 = (1 - a 2 n - b 2 n) y n + m - 3 + a 2 n T 2 n y n + m - 3 + b 2 n u 2 n,., y n + 2 = (1 - a (m - 2) n - b (m - 2) n) y n + 1 + a (m - 2) n T m - 2 n y n + 1 + b (m - 2) n u (m - 2) n, y n + 1 = (1 - a (m - 1) n - b (m - 1) n) y n + a (m - 1) n T m - 1 n y n + b (m - 1) n u (m - 1) n, y n = (1 - a m n - b m n) x n + a m n T m n x n + b m n u m n, m ≥ 2, n ≥ 1. The purpose of this paper is to study the above iteration scheme for approximating common fixed points of a finite family of asymptotically nonexpansive mappings and to prove weak and some strong convergence theorems for such mappings in real Banach spaces. The results obtained in this paper extend and improve some results in the existing literature. |
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