Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings

2005 ◽  
Vol 62 (6) ◽  
pp. 1149-1156 ◽  
Author(s):  
C.E. Chidume ◽  
Naseer Shahzad
Keyword(s):  
Strong Convergence ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Finite Family ◽  
Implicit Iteration Process ◽  
Implicit Iteration

scholarly journals Approximation of common fixed points of a finite family of Ø - demicontractive mappings by an implicit iteration method.

2015 ◽  
Vol 12 (1) ◽  
pp. 31-38
Author(s):  
DI Igbokwe ◽  
UE Udofia
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Iteration Method ◽  
Iteration Process ◽  
Common Fixed Points ◽  
Finite Family ◽  
Implicit Iteration Process ◽  
Demicontractive Mappings ◽  
Implicit Iteration

We prove that the Implicit Iteration process of Xu and Ori (2001) converges strongly to the commonfixed pointsof a finite family of Ø - demicontractive mappings in real Hilbertand Banachspaces. Our results extend the results of Osilike (2004a) from strictl pseudocontractive maps to the much more general Ø - demicontractive maps;complement and generalize several others in the literature.KEY WORDS AND PHRASES: Ø - Demicontractive Maps, Implicit Iteration Process, Fixed Points,Strong Convergence.

scholarly journals Hybrid Implicit Iteration Process for a Finite Family of Non-Self-Nonexpansive Mappings in Uniformly Convex Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Qiaohong Jiang ◽  
Jinghai Wang ◽  
Jianhua Huang
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Finite Family ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Uniformly Convex Banach Spaces ◽  
Implicit Iteration

Weak and strong convergence theorems are established for hybrid implicit iteration for a finite family of non-self-nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper extend and improve some recent results.

scholarly journals Strong Convergence of Non-Implicit Iteration Process with Errors in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Yan Hao ◽  
Xiaoshuang Wang ◽  
Aihua Tong
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Implicit Iteration Process ◽  
Implicit Iteration

The purpose of this paper is to study the strong convergence of a non-implicit iteration process with errors for asymptoticallyI-nonexpansive mappings in the intermediate sense in the framework of Banach spaces. The results presented in this paper extend and improve the corresponding results recently announced.

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