Generalized system for relaxed cocoercive mixed variational inequalities in Hilbert spaces

2009 ◽  
Vol 214 (1) ◽  
pp. 26-30 ◽  
Author(s):  
Zhenhua He ◽  
Feng Gu
Keyword(s):  
Variational Inequalities ◽  
Hilbert Spaces ◽  
Generalized System ◽  
Mixed Variational Inequalities

scholarly journals Generalized System for Relaxed Cocoercive Mixed Variational Inequalities and Iterative Algorithms in Hilbert Spaces

2012 ◽  
Vol 20 (3) ◽  
pp. 131-139
Author(s):  
Shuyi Zhang ◽  
Xinqi Guo ◽  
Dan Luan
Keyword(s):  
Variational Inequality ◽  
Hilbert Spaces ◽  
Resolvent Operator ◽  
Iterative Algorithms ◽  
Operator Technique ◽  
Mixed Variational Inequality ◽  
Generalized System ◽  
Resolvent Operator Technique ◽  
Mixed Variational Inequalities ◽  
The Resolvent Operator

Abstract The approximate solvability of a generalized system for relaxed co- coercive mixed variational inequality is studied by using the resolvent operator technique. The results presented in this paper extend and improve the main results of Chang et al.[1], He and Gu [2] and Verma [3, 4].

Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces

2008 ◽  
Vol 87 (4) ◽  
pp. 421-430 ◽  
Author(s):  
Xiaolong Qin ◽  
Shin Min Kang ◽  
Meijuan Shang
Keyword(s):  
Variational Inequalities ◽  
Hilbert Spaces ◽  
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 k-Steps Explicit Iterative Algorithms to Solve Generalized System of Nonlinear Mixed Variational Inequalities

2021 ◽  
pp. 131-148
Author(s):  
Sanjeev Gupta
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Iterative Algorithms ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Projection Operators ◽  
Generalized System ◽  
Convergence Results ◽  
Generalized Systems ◽  
Mixed Variational Inequalities

The objective of this paper is to consider new generalized systems of nonlinear mixed variational inequalities including 3k-distinct nonlinear relaxed cocoercive operators. We proposed k-steps explicit iterative methods including projection operators for this considered system and present the equivalent fixed point problem of this new generalized systems of variational inequalities. This equivalent fixed point problem suggest to us k-steps explicit iterative algorithms to obtain an approximate solution of the considered system. Convergence results of k-step explicit iterative algorithms are obtained.

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.

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