STRONG CONVERGENCE THEOREM OF A VISCOSITY PROCESS FOR A FINITE FAMILY OF TOTAL ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

2019 ◽  
Vol 14 (2) ◽  
pp. 57-75
Author(s):  
Agatha Chizoba Nnubia ◽  
M. Akabuike Nkiruka
Keyword(s):  
Strong Convergence ◽  
Convergence Theorem ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Strong Convergence Theorem ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Total Asymptotically Nonexpansive Mappings

scholarly journals On Unification of the Strong Convergence Theorems for a Finite Family of Total Asymptotically Nonexpansive Mappings in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Farrukh Mukhamedov ◽  
Mansoor Saburov
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Nonempty Closed Convex Subset ◽  
Finite Family ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Total Asymptotically Nonexpansive Mappings

We unify all known iterative methods by introducing a new explicit iterative scheme for approximation of common fixed points of finite families of total asymptoticallyI-nonexpansive mappings. Note that such a scheme contains a particular case of the method introduced by (C. E. Chidume and E. U. Ofoedu, 2009). We construct examples of total asymptotically nonexpansive mappings which are not asymptotically nonexpansive. Note that no such kind of examples were known in the literature. We prove the strong convergence theorems for such iterative process to a common fixed point of the finite family of total asymptoticallyI-nonexpansive and total asymptotically nonexpansive mappings, defined on a nonempty closed-convex subset of uniformly convex Banach spaces. Moreover, our results extend and unify all known 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.

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