scholarly journals Explicit iteration method for common fixed points of a finite family of nonself asymptotically nonexpansive mappings

2007 ◽  
Vol 53 (7) ◽  
pp. 1012-1019 ◽  
Author(s):  
Lin Wang
Keyword(s):  
Fixed Points ◽  
Iteration Method ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Finite Family ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive

scholarly journals Common Fixed Points Iteration Processes for a Finite Family of Asymptotically Nonexpansive Mappings

2004 ◽  
Vol 11 (1) ◽  
pp. 83-92
Author(s):  
Jui-Chi Huang
Keyword(s):  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Nonempty Closed Convex Subset ◽  
Convex Banach Space ◽  
Finite Family ◽  
Uniformly Convex ◽  
Asymptotically Nonexpansive ◽  
Iteration Processes ◽  
Suitable Sequence

Abstract Let 𝐸 be a uniformly convex Banach space which satisfies Opial's condition or its dual 𝐸* has the Kadec–Klee property, 𝐶 a nonempty closed convex subset of 𝐸, and 𝑇𝑗 : 𝐶 → 𝐶 an asymptotically nonexpansive mapping for each 𝑗 = 1, 2, . . . , 𝑟. Suppose {𝑥𝑛} is generated iteratively by where 𝑈𝑛(0) = 𝐼, 𝐼 is the identity map and {α 𝑛(𝑗)} is a suitable sequence in [0, 1]. If the set of common fixed points of is nonempty, then weak convergence of {𝑥𝑛} to some is obtained.

scholarly journals Convergence of two-step iterative scheme with errors for two asymptotically nonexpansive mappings

2004 ◽  
Vol 2004 (37) ◽  
pp. 1965-1971 ◽  
Author(s):  
Hafiz Fukhar-ud-din ◽  
Safeer Hussain Khan
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Weak And Strong Convergence ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
The Common

A two-step iterative scheme with errors has been studied to approximate the common fixed points of two asymptotically nonexpansive mappings through weak and strong convergence in Banach spaces.

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.

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