scholarly journals Stability with respect to the domain of a nonlinear variational inequality

2003 ◽  
Vol 4 (1) ◽  
pp. 25
Author(s):  
Daniela Inoan
Keyword(s):  
Variational Inequality ◽  
Nonlinear Variational Inequality

scholarly journals Generalized nonlinear variational inequality problems involving multivalued mappings

1997 ◽  
Vol 10 (3) ◽  
pp. 289-295 ◽  
Author(s):  
Ram U. Verma
Keyword(s):  
Variational Inequality ◽  
Variational Inequality Problems ◽  
Multivalued Mappings ◽  
Strongly Monotone ◽  
Nonlinear Variational Inequality

The solvability of a class of generalized nonlinear variational inequality problems involving multivalued, strongly monotone and strongly Lipschitz (a special type) operators, which are closely associated with generalized nonlinear complementarily problems, is discussed.

scholarly journals On a general nonlinear variational inequality

1990 ◽  
Vol 42 (3) ◽  
pp. 399-406 ◽  
Author(s):  
Ramendra Krishna Bose
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Existence And Uniqueness ◽  
Additional Condition ◽  
Existence Of Solution ◽  
Uniqueness Of Solutions ◽  
Science And Engineering ◽  
Inequality Theory ◽  
Fixed Point Technique ◽  
Nonlinear Variational Inequality

Variational inequality theory provides techniques for solving a variety of applied problems in science and engineering. Recently Noor considered some interesting general nonlinear and linear variational inequalities in a series of papers and proved the existence and uniqueness of solutions by a fixed point technique developed by Glowinski, Lions and Tremolieres and also by a fixed point technique of Lions and Stampacchia. But there are several inaccuracies in his proofs and here they have been removed and correct formulation of the theorems are stated and proved and relationships are clearly shown. The existence of solution necessitates an additional condition in one case, and less condition in the other, but uniqueness can be proved without the condition that the operator be antimonotone.

scholarly journals A Generalized System of Nonlinear Variational Inequalities in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Prapairat Junlouchai ◽  
Anchalee Kaewcharoen ◽  
Somyot Plubtieng
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Generalized System ◽  
Uniformly Smooth ◽  
Strictly Convex Banach Spaces ◽  
Generalized Projection Method ◽  
Nonlinear Variational Inequality

We introduce a new generalized system of nonlinear variational inequality problems (GSNVIP) by using the generalized projection method. Moreover, we introduce an iterative scheme for finding a solution to this problem. Moreover, some existence and strong convergence theorems are established in uniformly smooth and strictly convex Banach spaces under suitable conditions. The results presented in the paper improve and extend some recent results.

scholarly journals Algorithms for a System of General Variational Inequalities in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Jin-Hua Zhu ◽  
Shih-Sen Chang ◽  
Min Liu
Keyword(s):  
Variational Inequality ◽  
Banach Spaces ◽  
Existence Theorems ◽  
Extragradient Method ◽  
Finite Family ◽  
Existence Problem ◽  
Special Cases ◽  
General Variational Inequalities ◽  
Solvability Problem ◽  
Nonlinear Variational Inequality

The purpose of this paper is using Korpelevich's extragradient method to study the existence problem of solutions and approximation solvability problem for a class of systems of finite family of general nonlinear variational inequality in Banach spaces, which includes many kinds of variational inequality problems as special cases. Under suitable conditions, some existence theorems and approximation solvability theorems are proved. The results presented in the paper improve and extend some recent results.

scholarly journals Weighted Method for Uncertain Nonlinear Variational Inequality Problems

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 974
Author(s):  
Cunlin Li ◽  
Mihai Postolache ◽  
Zhifu Jia
Keyword(s):  
Variational Inequality ◽  
Approximation Method ◽  
Uncertain Variable ◽  
Variational Inequality Problems ◽  
Event Space ◽  
Residual Function ◽  
Compact Approximation ◽  
Global Optimal ◽  
Residual Minimization ◽  
Nonlinear Variational Inequality

A convex combined expectations regularized gap function with uncertain variable is presented to deal with uncertain nonlinear variational inequality problems (UNVIP). The UNVIP is transformed into a minimization problem through an uncertain weighted expected residual function. Moreover, the convergence of the global optimal solutions of the uncertain weighted expected residual minimization model is given through the integration by parts method under the compact space of the uncertain event. The limiting behaviors of the transformed model are analyzed. Furthermore, a compact approximation method is proposed in the unbounded uncertain event space. Through analysis of the convergence of UWERM model and reasonable hypothesis, the compact approximation method is verified under the circumstance of Holder continuity.

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