scholarly journals System of General Variational Inequalities Involving Different Nonlinear Operators Related to Fixed Point Problems and Its Applications

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Issara Inchan ◽  
Narin Petrot
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Fixed Point Problems ◽  
Nonlinear Operators ◽  
General Variational Inequalities

scholarly journals Gauss-Seidel type algorithms for a class of variational inequalities

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 395-407
Author(s):  
Muhammad Noor ◽  
Awais Khan ◽  
Khalida Noor ◽  
Amjad Pervez
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Projection Operator ◽  
Fixed Point Problems ◽  
Operator Technique ◽  
Equivalent Formulation ◽  
Nonlinear Operators ◽  
Special Cases ◽  
Projection Operator Technique ◽  
New System

In this paper, we consider a new system of extended general quasi variational inequalities involving six nonlinear operators. Using projection operator technique, we show that system of extended general quasi variational inequalities is equivalent to a system of fixed point problems. Using this alternative equivalent formulation, we propose and analyze Gauss-Seidel type algorithms for solving a system of extended general quasi variational inequalities. Convergence of new method is discussed under some suitable conditions. Several special cases are discussed. Results obtained in this paper continue to hold for these problems.

scholarly journals Systems of Variational Inequalities with Nonlinear Operators

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 338 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Qing Yuan
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
General System ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Nonlinear Operators ◽  
Pseudocontractive Mappings ◽  
Common Fixed Point Problem

In this work, we concern ourselves with the problem of solving a general system of variational inequalities whose solutions also solve a common fixed-point problem of a family of countably many nonlinear operators via a hybrid viscosity implicit iteration method in 2 uniformly smooth and uniformly convex Banach spaces. An application to common fixed-point problems of asymptotically nonexpansive and pseudocontractive mappings and variational inequality problems for strict pseudocontractive mappings is also given in Banach spaces.

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