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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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30280/1/30280.pdf |
| _version_ | 1796971709359718400 |
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| author | Temir, Seyit Kilicman, Adem |
| author_facet | Temir, Seyit Kilicman, Adem |
| author_sort | Temir, Seyit |
| collection | UPM |
| description | 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. |
| first_indexed | 2024-03-06T08:17:05Z |
| format | Article |
| id | upm.eprints-30280 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:17:05Z |
| publishDate | 2013 |
| publisher | Hindawi Publishing Corporation |
| record_format | dspace |
| spelling | upm.eprints-302802017-10-20T03:32:35Z http://psasir.upm.edu.my/id/eprint/30280/ Approximating common fixed points for a finite family of asymptotically nonexpansive mappings using iteration process with errors terms Temir, Seyit Kilicman, Adem 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. Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30280/1/30280.pdf Temir, Seyit and Kilicman, Adem (2013) Approximating common fixed points for a finite family of asymptotically nonexpansive mappings using iteration process with errors terms. Abstract and Applied Analysis, 2013. art. no. 974317. pp. 1-8. ISSN 1085-3375; ESSN: 1687-0409 http://www.hindawi.com/journals/aaa/2013/974317/ 10.1155/2013/974317 |
| spellingShingle | Temir, Seyit Kilicman, Adem Approximating common fixed points for a finite family of asymptotically nonexpansive mappings using iteration process with errors terms |
| title | Approximating common fixed points for a finite family of asymptotically nonexpansive mappings using iteration process with errors terms |
| title_full | Approximating common fixed points for a finite family of asymptotically nonexpansive mappings using iteration process with errors terms |
| title_fullStr | Approximating common fixed points for a finite family of asymptotically nonexpansive mappings using iteration process with errors terms |
| title_full_unstemmed | Approximating common fixed points for a finite family of asymptotically nonexpansive mappings using iteration process with errors terms |
| title_short | Approximating common fixed points for a finite family of asymptotically nonexpansive mappings using iteration process with errors terms |
| title_sort | approximating common fixed points for a finite family of asymptotically nonexpansive mappings using iteration process with errors terms |
| url | http://psasir.upm.edu.my/id/eprint/30280/1/30280.pdf |
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