scholarly journals Wiener-Hopf Equations Technique for General Variational Inequalities Involving Relaxed Monotone Mappings and Nonexpansive Mappings

2007 ◽  
Vol 2007 (1) ◽  
pp. 064947
Author(s):  
Yongfu Su ◽  
Meijuan Shang ◽  
Xiaolong Qin
Keyword(s):  
Variational Inequalities ◽  
Nonexpansive Mappings ◽  
Monotone Mappings ◽  
General Variational Inequalities

scholarly journals Modified Relaxed Extragradient Method for a General System of Variational Inequalities and Nonexpansive Mappings in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yuanheng Wang ◽  
Liu Yang
Keyword(s):  
Variational Inequalities ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Extragradient Method ◽  
General System ◽  
Iterative Sequence ◽  
Monotone Mappings ◽  
System Of Variational Inequalities ◽  
Common Solution ◽  
Demiclosedness Principle

The purpose of this paper is to introduce a new modified relaxed extragradient method and study for finding some common solutions for a general system of variational inequalities with inversestrongly monotone mappings and nonexpansive mappings in the framework of real Banach spaces. By using the demiclosedness principle, it is proved that the iterative sequence defined by the relaxed extragradient method converges strongly to a common solution for the system of variational inequalities and nonexpansive mappings under quite mild conditions.

scholarly journals Viscosity Iterative Schemes for Finding Split Common Solutions of Variational Inequalities and Fixed Point Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Zhenhua He ◽  
Wei-Shih Du
Keyword(s):  
Variational Inequalities ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Monotone Mappings ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Iterative Schemes ◽  
Inverse Strongly Monotone ◽  
Strongly Monotone Mappings

We introduce some new iterative schemes based on viscosity approximation method for finding a split common element of the solution set of a pair of simultaneous variational inequalities for inverse strongly monotone mappings in real Hilbert spaces with a family of infinitely nonexpansive mappings. Some strong convergence theorems are also given. Our results generalize and improve some well-known results in the literature and references therein.

scholarly journals Hybrid Algorithms for Solving Variational Inequalities, Variational Inclusions, Mixed Equilibria, and Fixed Point Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-22 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Adrian Petrusel ◽  
Mu-Ming Wong ◽  
Jen-Chih Yao
Keyword(s):  
Variational Inequalities ◽  
Iterative Algorithm ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Extragradient Method ◽  
Finite Family ◽  
Steepest Descent Method ◽  
Common Element ◽  
Monotone Mappings ◽  
Mixed Equilibria

We present a hybrid iterative algorithm for finding a common element of the set of solutions of a finite family of generalized mixed equilibrium problems, the set of solutions of a finite family of variational inequalities for inverse strong monotone mappings, the set of fixed points of an infinite family of nonexpansive mappings, and the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed hybrid iterative algorithm has strong convergence under some mild conditions imposed on algorithm parameters. Here, our hybrid algorithm is based on Korpelevič’s extragradient method, hybrid steepest-descent method, and viscosity approximation method.

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