Projection methods for a generalized system of nonconvex variational inequalities with different nonlinear operators

2010 ◽  
Vol 73 (7) ◽  
pp. 2292-2297 ◽  
Author(s):  
Dao-Jun Wen
Keyword(s):  
Variational Inequalities ◽  
Projection Methods ◽  
Nonlinear Operators ◽  
Generalized System

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 Two-Step Systems for G-H-Relaxed Pseudococoercive Nonlinear Variational Problems Based on Projection Methods

2005 ◽  
Vol 12 (1) ◽  
pp. 1-10
Author(s):  
Ravi P. Agarwal ◽  
Donal O'Regan ◽  
Ram U. Verma
Keyword(s):  
Variational Inequalities ◽  
Hilbert Spaces ◽  
Variational Problems ◽  
Projection Methods ◽  
Strongly Monotone ◽  
Generalized System ◽  
Nonlinear Mappings ◽  
Convex Subsets

Abstract The approximation-solvability of a generalized system of nonlinear variational inequalities (SNVI) involving relaxed pseudococoercive mappings, based on the convergence of a system of projection methods, is presented. The class of relaxed pseudococoercive mappings is more general than classes of strongly monotone and relaxed cocoercive mappings. Let 𝐾1 and 𝐾2 be nonempty closed convex subsets of real Hilbert spaces 𝐻1 and 𝐻2, respectively. The two-step SNVI problem considered here is as follows: find an element (𝑥*, 𝑦*) ∈ 𝐻1 × 𝐻2 such that (𝑔(𝑥*), 𝑔(𝑦*)) ∈ 𝐾1 × 𝐾2 and where 𝑆 : 𝐻1 × 𝐻2 → 𝐻1, 𝑇 : 𝐻1 × 𝐻2 → 𝐻2, 𝑔 : 𝐻1 → 𝐻1 and ℎ : 𝐻2 → 𝐻2 are nonlinear mappings.

scholarly journals Inertial projection methods for solving general quasi-variational inequalities

2021 ◽  
Vol 6 (2) ◽  
pp. 1075-1086
Author(s):  
Saudia Jabeen ◽  
◽  
Bandar B. Mohsen ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
...  
Keyword(s):  
Variational Inequalities ◽  
Projection Methods
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