scholarly journals Strong convergence of a modified implicit iteration process for a finite family ofZ-operators

2006 ◽  
Vol 2006 ◽  
pp. 1-6
Author(s):  
Arif Rafiq
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Iteration Process ◽  
Finite Family ◽  
Implicit Iteration Process ◽  
Implicit Iteration

The purpose of this note is to establish a strong convergence of a modified implicit iteration process to a common fixed point for a finite family ofZ-operators.

scholarly journals A new implicit iteration process for two strongly pseudocontractive mappings

2012 ◽  
Vol 21 (2) ◽  
pp. 197-201
Author(s):  
ARIF RAFIQ ◽  
◽  
ANA MARIA ACU ◽  
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Iteration Process ◽  
Implicit Iteration Process ◽  
Pseudocontractive Mappings ◽  
Implicit Iteration

The purpose of this paper is to establish the strong convergence of an implicit iteration process to a common fixed point for two continuous strongly pseudocontractive mappings.

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.

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