Halpern projection methods for solving pseudomonotone multivalued variational inequalities in Hilbert spaces

2020 ◽  
Author(s):  
Pham Ngoc Anh ◽  
T. V. Thang ◽  
H. T. C. Thach
Keyword(s):  
Variational Inequalities ◽  
Hilbert Spaces ◽  
Projection Methods ◽  
Multivalued Variational Inequalities

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 Projection Methods for a System of Nonlinear Mixed Variational Inequalities in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Zhong-Bao Wang ◽  
Guo-Ji Tang ◽  
Hong-Ling Zhang
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Projection Operator ◽  
Existence And Uniqueness ◽  
Projection Methods ◽  
Uniqueness Of Solution ◽  
Mixed Variational Inequality ◽  
Mixed Variational Inequalities

The existence and uniqueness of solution for a system of nonlinear mixed variational inequality in Banach spaces is given firstly. A Mann iterative sequences with errors for this system of nonlinear mixed variational inequalities in Banach spaces is studied, by using the generalizedf-projection operatorπKf. Our results extend the main results in (Verma (2005); Verma (2001)) from Hilbert spaces to Banach spaces.

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.

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