scholarly journals Convergence Theorems for Total Asymptotically Nonexpansive Mappings in Hyperbolic Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Liang-cai Zhao ◽  
Shih-sen Chang ◽  
Xiong Rui Wang
Keyword(s):  
Current Literature ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Hyperbolic Spaces ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Total Asymptotically Nonexpansive Mappings

The purpose of this paper is to introduce the concept oftotal asymptotically nonexpansive mappingsand to prove someΔ-convergence theorems of the iteration process for this kind of mappings in the setting ofhyperbolic spaces. The results presented in the paper extend and improve some recent results announced in the current literature.

scholarly journals -Convergence Problems for Asymptotically Nonexpansive Mappings in CAT(0) Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Luo Yi Shi ◽  
Ru Dong Chen ◽  
Yu Jing Wu
Keyword(s):  
Fixed Point ◽  
Convex Subset ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Convergence Problems

New △-convergence theorems of iterative sequences for asymptotically nonexpansive mappings in CAT(0) spaces are obtained. Consider an asymptotically nonexpansive self-mapping of a closed convex subset of a CAT(0) space . Consider the iteration process , where is arbitrary and or for , where . It is shown that under certain appropriate conditions on   △-converges to a fixed point of .

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.

Strong and weak convergence theorems for fixed points of a class of nonlinear mappings

2014 ◽  
Vol 64 (2) ◽  
Author(s):  
Changqun Wu ◽  
Zhiqiang Wei ◽  
Yu Li
Keyword(s):  
Weak Convergence ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Projection Methods ◽  
Convergence Theorems ◽  
Strong And Weak Convergence ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Total Asymptotically Nonexpansive Mappings ◽  
Weak Convergence Theorem

AbstractIn this paper, the class of total asymptotically nonexpansive mappings is considered. A weak convergence theorem of Mann-type iterative algorithm is established. Hybrid projection methods are considered for the class of total asymptotically nonexpansive mappings. Strong convergence theorems are also established in the framework of Hilbert spaces.

Sign in / Sign up

Export Citation Format

Share Document