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Approximating Common Fixed Points for a Finite Family of Asymptotically Nonexpansive Mappings Using Iteration Process with Errors Terms
Joint Authors
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-12-24
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Temir, Seyit& Kiliçman, Adem. 2013. Approximating Common Fixed Points for a Finite Family of Asymptotically Nonexpansive Mappings Using Iteration Process with Errors Terms. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-8.
https://search.emarefa.net/detail/BIM-512762
Modern Language Association (MLA)
Temir, Seyit& Kiliçman, Adem. Approximating Common Fixed Points for a Finite Family of Asymptotically Nonexpansive Mappings Using Iteration Process with Errors Terms. Abstract and Applied Analysis No. 2013 (2013), pp.1-8.
https://search.emarefa.net/detail/BIM-512762
American Medical Association (AMA)
Temir, Seyit& Kiliçman, Adem. Approximating Common Fixed Points for a Finite Family of Asymptotically Nonexpansive Mappings Using Iteration Process with Errors Terms. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-8.
https://search.emarefa.net/detail/BIM-512762
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-512762