General Wiener–Hopf equation technique for nonexpansive mappings and general variational inequalities in Hilbert spaces

2008 ◽  
Vol 201 (1-2) ◽  
pp. 716-722 ◽  
Author(s):  
Xiaolong Qin ◽  
Muhammad Aslam Noor
Keyword(s):  
Variational Inequalities ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Hopf Equation ◽  
General Variational Inequalities

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.

Generalized System for Relaxed Cocoercive and Involving Projective Nonexpansive Mapping Variational Inequalities

2011 ◽  
Vol 393-395 ◽  
pp. 792-795
Author(s):  
Guang Hui Gu ◽  
Yong Fu Su
Keyword(s):  
Variational Inequalities ◽  
Nonexpansive Mapping ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Projection Methods ◽  
Generalized System

Firstly, the concept of projective nonexpansive mappings is presented in this paper. The approximate solvability of a generalized system for relaxed cocoercive and involving projective nonexpansive mapping nonlinear variational inequalities in Hilbert spaces is studied, based on the convergence of projection methods. The results presented in this paper extend and improve the main results of many authors.

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.

Sign in / Sign up

Export Citation Format

Share Document