scholarly journals Convergence of a General Composite Iterative Method for a Countable Family of Nonexpansive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Shuang Wang
Keyword(s):  
Iterative Method ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Countable Family

We propose a general composite iterative method for computing common fixed points of a countable family of nonexpansive mappings in the framework of Hilbert spaces. Our results improve and complement the corresponding ones announced by many others.

scholarly journals On the viscosity rule for common fixed points of two nonexpansive mappings in Hilbert spaces

2017 ◽  
Vol 1 (1) ◽  
pp. 111-125 ◽  
Author(s):  
Sayed Fakhar Abbas Naqvi ◽  
◽  
Muhammad Saqib Khan ◽  
Keyword(s):  
Fixed Points ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Common Fixed Points

scholarly journals Hybrid Mann Viscosity Implicit Iteration Methods for Triple Hierarchical Variational Inequalities, Systems of Variational Inequalities and Fixed Point Problems

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 142 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Qing Yuan
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
General System ◽  
Inequality Constraint ◽  
Common Fixed Points ◽  
Common Solution ◽  
Implicit Iteration

In the present work, we introduce a hybrid Mann viscosity-like implicit iteration to find solutions of a monotone classical variational inequality with a variational inequality constraint over the common solution set of a general system of variational inequalities and a problem of common fixed points of an asymptotically nonexpansive mapping and a countable of uniformly Lipschitzian pseudocontractive mappings in Hilbert spaces, which is called the triple hierarchical constrained variational inequality. Strong convergence of the proposed method to the unique solution of the problem is guaranteed under some suitable assumptions. As a sub-result, we provide an algorithm to solve problem of common fixed points of pseudocontractive, nonexpansive mappings, variational inequality problems and generalized mixed bifunction equilibrium problems in Hilbert spaces.

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