scholarly journals A PARALLEL HYBRID METHOD FOR EQUILIBRIUM PROBLEMS, VARIATIONAL INEQUALITIES AND NONEXPANSIVE MAPPINGS IN HILBERT SPACE

2015 ◽  
Vol 52 (2) ◽  
pp. 373-388 ◽  
Author(s):  
Dang Van Hieu
Keyword(s):  
Hilbert Space ◽  
Variational Inequalities ◽  
Hybrid Method ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Parallel Hybrid

scholarly journals Shrinking Extragradient Method for Pseudomonotone Equilibrium Problems and Quasi-Nonexpansive Mappings

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 480
Author(s):  
Manatchanok Khonchaliew ◽  
Ali Farajzadeh ◽  
Narin Petrot
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Numerical Experiments ◽  
Equilibrium Problems ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Extragradient Method ◽  
Constraint Qualifications ◽  
Solution Sets ◽  
New Algorithms

This paper presents two shrinking extragradient algorithms that can both find the solution sets of equilibrium problems for pseudomonotone bifunctions and find the sets of fixed points of quasi-nonexpansive mappings in a real Hilbert space. Under some constraint qualifications of the scalar sequences, these two new algorithms show strong convergence. Some numerical experiments are presented to demonstrate the new algorithms. Finally, the two introduced algorithms are compared with a standard, well-known algorithm.

scholarly journals Fixed Points Approximation and Solutions of Some Equilibrium and Variational Inequalities Problems

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Bashir Ali
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Fixed Points ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Strong Convergence Theorem ◽  
Points Approximation

We prove a new strong convergence theorem for an element in the intersection of the set of common fixed points of a countable family of nonexpansive mappings, the set of solutions of some variational inequality problems, and the set of solutions of some equilibrium problems using a new iterative scheme. Our theorem generalizes and improves some recent results.

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