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 Ti:K→K (i=1,2,…,m) be m asymptotically nonexpansive mappings with sequence {kn}⊂[1, ∞), ∑n=1∞(kn-1)<∞, and ℱ=⋂i=1mF(Ti)≠∅, where F is the set of fixed points of Ti. Suppose that {ain}n=1∞, {bin}n=1∞, i=1,2,…,m are app...
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/974317 |
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| author | Seyit Temir Adem Kiliçman |
| author_facet | Seyit Temir Adem Kiliçman |
| author_sort | Seyit Temir |
| collection | DOAJ |
| description | Let X be a real Banach space and K a nonempty closed convex subset of X. Let Ti:K→K (i=1,2,…,m) be m asymptotically nonexpansive mappings with sequence {kn}⊂[1, ∞), ∑n=1∞(kn-1)<∞, and ℱ=⋂i=1mF(Ti)≠∅, where F is the set of fixed points of Ti. Suppose that {ain}n=1∞, {bin}n=1∞, i=1,2,…,m are appropriate sequences in [0,1] and {uin}n=1∞, i=1,2,…,m are bounded sequences in K such that ∑n=1∞bin<∞ for i=1,2,…,m. We give {xn} defined by x1∈K,xn+1=(1-a1n-b1n)yn+m-2+a1nT1nyn+m-2+b1nu1n,yn+m-2=(1-a2n-b2n)yn+m-3+a2nT2nyn+m-3 +b2nu2n,…,yn+2=(1-a(m-2)n-b(m-2)n)yn+1+a(m-2)nTm-2nyn+1+b(m-2)nu(m-2)n,yn+1=(1-a(m-1)n -b(m-1)n)yn+a(m-1)nTm-1nyn+b(m-1)nu(m-1)n,yn=(1-amn-bmn)xn+amnTmnxn+bmnumn,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. |
| format | Article |
| id | doaj-art-622a53ba2e2b455d8b5008de641706bb |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-622a53ba2e2b455d8b5008de641706bb2025-02-03T06:07:52ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/974317974317Approximating Common Fixed Points for a Finite Family of Asymptotically Nonexpansive Mappings Using Iteration Process with Errors TermsSeyit Temir0Adem Kiliçman1Department of Mathematics, Arts and Science Faculty, Harran University, 63200 Şanliurfa, TurkeyDepartment of Mathematics and Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Selangor, MalaysiaLet X be a real Banach space and K a nonempty closed convex subset of X. Let Ti:K→K (i=1,2,…,m) be m asymptotically nonexpansive mappings with sequence {kn}⊂[1, ∞), ∑n=1∞(kn-1)<∞, and ℱ=⋂i=1mF(Ti)≠∅, where F is the set of fixed points of Ti. Suppose that {ain}n=1∞, {bin}n=1∞, i=1,2,…,m are appropriate sequences in [0,1] and {uin}n=1∞, i=1,2,…,m are bounded sequences in K such that ∑n=1∞bin<∞ for i=1,2,…,m. We give {xn} defined by x1∈K,xn+1=(1-a1n-b1n)yn+m-2+a1nT1nyn+m-2+b1nu1n,yn+m-2=(1-a2n-b2n)yn+m-3+a2nT2nyn+m-3 +b2nu2n,…,yn+2=(1-a(m-2)n-b(m-2)n)yn+1+a(m-2)nTm-2nyn+1+b(m-2)nu(m-2)n,yn+1=(1-a(m-1)n -b(m-1)n)yn+a(m-1)nTm-1nyn+b(m-1)nu(m-1)n,yn=(1-amn-bmn)xn+amnTmnxn+bmnumn,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.http://dx.doi.org/10.1155/2013/974317 |
| spellingShingle | Seyit Temir Adem Kiliçman Approximating Common Fixed Points for a Finite Family of Asymptotically Nonexpansive Mappings Using Iteration Process with Errors Terms Abstract and Applied Analysis |
| 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://dx.doi.org/10.1155/2013/974317 |
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