scholarly journals Strong and Weak Convergence of Implicit Iterative Process with Errors for Asymptotically Nonexpansive Mappings

2006 ◽  
Vol 12 (2) ◽  
Author(s):  
F. Gu
Keyword(s):  
Weak Convergence ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Strong And Weak Convergence ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive

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.

scholarly journals On the JK Iterative Process in Banach Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Junaid Ahmad ◽  
Hüseyin Işık ◽  
Faeem Ali ◽  
Kifayat Ullah ◽  
Eskandar Ameer ◽  
...  
Keyword(s):  
Weak Convergence ◽  
Banach Spaces ◽  
Iterative Process ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
The Other ◽  
Iterative Schemes ◽  
Strong And Weak Convergence ◽  
Nonexpansive Maps ◽  
Iterative Procedures

In the recent progress, different iterative procedures have been constructed in order to find the fixed point for a given self-map in an effective way. Among the other things, an effective iterative procedure called the JK iterative scheme was recently constructed and its strong and weak convergence was established for the class of Suzuki mappings in the setting of Banach spaces. The first purpose of this research is to obtain the strong and weak convergence of this scheme in the wider setting of generalized α -nonexpansive mappings. Secondly, by constructing an example of generalized α -nonexpansive maps which is not a Suzuki map, we show that the JK iterative scheme converges faster as compared the other iterative schemes. The presented results of this paper properly extend and improve the corresponding results of the literature.

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