A new general system of variational inequalities for convergence theorem and application

2018 ◽  
Vol 81 (1) ◽  
pp. 99-123 ◽  
Author(s):  
Keerati Siriyan ◽  
Atid Kangtunyakarn
Keyword(s):  
Variational Inequalities ◽  
Convergence Theorem ◽  
General System ◽  
System Of Variational Inequalities

scholarly journals Hybrid Projection Algorithm for a New General System of Variational Inequalities in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-22
Author(s):  
S. Imnang
Keyword(s):  
Hilbert Space ◽  
Variational Inequalities ◽  
Nonexpansive Mapping ◽  
Real Hilbert Space ◽  
General System ◽  
Projection Algorithm ◽  
Common Element ◽  
System Of Variational Inequalities ◽  
Demiclosedness Principle ◽  
Hybrid Projection Algorithm

A new general system of variational inequalities in a real Hilbert space is introduced and studied. The solution of this system is shown to be a fixed point of a nonexpansive mapping. We also introduce a hybrid projection algorithm for finding a common element of the set of solutions of a new general system of variational inequalities, the set of solutions of a mixed equilibrium problem, and the set of fixed points of a nonexpansive mapping in a real Hilbert space. Several strong convergence theorems of the proposed hybrid projection algorithm are established by using the demiclosedness principle. Our results extend and improve recent results announced by many others.

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