scholarly journals On Strong Convergence by the Hybrid Method for Equilibrium and Fixed Point Problems for an Inifnite Family of Asymptotically Nonexpansive Mappings

2009 ◽  
Vol 2009 (1) ◽  
pp. 798319
Author(s):  
Gang Cai ◽  
Changsong Hu
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Hybrid Method ◽  
Nonexpansive Mappings ◽  
Fixed Point Problems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive

scholarly journals Strong Convergence Theorems for Two Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xi-bing He ◽  
Xiao-jian Hui ◽  
Hui Xing
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Mathematical Programming ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Hybrid Method ◽  
Nonexpansive Mappings ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive

The purpose of this paper is to establish some strong convergence theorems for a common fixed point of two total quasi-ϕ-asymptotically nonexpansive mappings in Banach space by means of the hybrid method in mathematical programming. The results presented in this paper extend and improve on the corresponding ones announced by Martinez-Yanes and Xu (2006), Plubtieng and Ungchittrakool (2007), Qin et al. (2009), and many others.

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 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 Theorems for a Countable Family of Lipschitzian Mappings

2010 ◽  
Vol 2010 ◽  
pp. 1-17
Author(s):  
Weerayuth Nilsrakoo ◽  
Satit Saejung
Keyword(s):  
Iterative Method ◽  
Strong Convergence ◽  
Hybrid Method ◽  
Nonexpansive Mappings ◽  
Countable Family ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Lipschitzian Mappings ◽  
Asymptotically Nonexpansive ◽  
Special Cases

We modify the iterative method introduced by Kim and Xu (2006) for a countable family of Lipschitzian mappings by the hybrid method of Takahashi et al. (2008). Our results include recent ones concerning asymptotically nonexpansive mappings due to Plubtieng and Ungchittrakool (2007) and Zegeye and Shahzad (2008, 2010) as special cases.

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