scholarly journals Strong Convergence Theorem of Implicit Iteration Process for Generalized Asymptotically Nonexpansive Mappings in Hilbert Space

2008 ◽  
Vol 2008 ◽  
pp. 1-9
Author(s):  
Lili He ◽  
Lei Deng ◽  
Jianjun Liu
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Strong Convergence Theorem ◽  
Implicit Iteration Process ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Implicit Iteration

LetCbe a nonempty closed and convex subset of a Hilbert spaceH, letTandS:C→Cbe two commutative generalized asymptotically nonexpansive mappings. We introduce an implicit iteration process ofSandTdefined byxn=αnx0+(1−αn)(2/((n+1)(n+2)))∑k=0n∑i+j=kSiTjxn, and then prove that{xn}converges strongly to a common fixed point ofSandT. The results generalize and unify the corresponding results.

scholarly journals Strong Convergence Theorem for Two Commutative Asymptotically Nonexpansive Mappings in Hilbert Space

2008 ◽  
Vol 2008 ◽  
pp. 1-9
Author(s):  
Jianjun Liu ◽  
Lili He ◽  
Lei Deng
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Hybrid Method ◽  
Convex Subset ◽  
Convergence Theorem ◽  
Nonexpansive Mappings ◽  
Strong Convergence Theorem ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive

Cis a bounded closed convex subset of a Hilbert spaceH,TandS:C→Care two asymptotically nonexpansive mappings such thatST=TS. We establish a strong convergence theorem forSandTin Hilbert space by hybrid method. The results generalize and unify many corresponding results.

scholarly journals Convergence of an implicit iteration process with errors for two asymptotically nonexpansive mappings

2013 ◽  
Vol 46 (4) ◽  
Author(s):  
Seyit Temir
Keyword(s):  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Iterative Algorithms ◽  
Iteration Process ◽  
Weak And Strong Convergence ◽  
Implicit Iteration Process ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Implicit Iteration ◽  
Appl Math

AbstractThe purpose of this paper is to introduce an implicit iterative process with errors for approximating common fixed point of two finite families of asymptotically nonexpansive mappings in the framework of Banach space. The results presented in this paper extend and generalize the corresponding results of Qin et al. [Convergence analysis of implicit iterative algorithms for asymptotically nonexpansive mappings, Appl. Math. Comp. 210 (2009), 542–550], Thakur [Weak and strong convergence of composite implicit iteration process, Appl. Math. Comp. 190 (2007), 965–973] and some others.

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