scholarly journals A New System of Multivalued Mixed Variational Inequality Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Xi Li ◽  
Xue-song Li
Keyword(s):  
Variational Inequality ◽  
Variational Inequality Problem ◽  
Existence Of Solutions ◽  
Projection Algorithm ◽  
Mixed Variational Inequality ◽  
Inequality Problem ◽  
Special Cases ◽  
Systems Of Variational Inequalities ◽  
Special Case ◽  
New System

We consider a new system of multivalued mixed variational inequality problem, which includes some known systems of variational inequalities as special cases. Under suitable conditions, the existence of solutions for the system of multivalued mixed variational inequality problem and the convergence of iterative sequences generated by the generalizedf-projection algorithm are proved. A perturbational algorithm for solving a special case of multivalued mixed variational inequality problem is formally constructed. The results concerned with the existence of solutions and the convergence of iterative sequences generated by the perturbational algorithm are also given. Some known results are improved and generalized.

scholarly journals Existence Results for Vector Mixed Quasi-Complementarity Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Suhel Ahmad Khan ◽  
Naeem Ahmad
Keyword(s):  
Variational Inequality ◽  
Banach Spaces ◽  
Variational Inequality Problem ◽  
Existence Of Solutions ◽  
Complementarity Problems ◽  
Existence Results ◽  
Variational Inequality Problems ◽  
Inequality Problem ◽  
Quasi Variational Inequality

We introduce strong vector mixed quasi-complementarity problems and the corresponding strong vector mixed quasi-variational inequality problems. We establish equivalence between strong mixed quasi-complementarity problems and strong mixed quasi-variational inequality problem in Banach spaces. Further, using KKM-Fan lemma, we prove the existence of solutions of these problems, under pseudomonotonicity assumption. The results presented in this paper are extensions and improvements of some earlier and recent results in the literature.

scholarly journals Split general quasi-variational inequality problem

2015 ◽  
Vol 22 (3) ◽  
Author(s):  
Kaleem Raza Kazmi
Keyword(s):  
Variational Inequality ◽  
Variational Inequality Problem ◽  
Natural Extension ◽  
Iterative Algorithms ◽  
Variational Inequality Problems ◽  
Convergence Criteria ◽  
Inequality Problem ◽  
Special Cases ◽  
Quasi Variational Inequality ◽  
Split Variational Inequality Problem

AbstractIn this paper, we introduce a split general quasi-variational inequality problem which is a natural extension of a split variational inequality problem, quasivariational and variational inequality problems in Hilbert spaces. Using the projection method, we propose an iterative algorithm for a split general quasi-variational inequality problem and discuss some special cases. Further, we discuss the convergence criteria of these iterative algorithms. The results presented in this paper generalize, unify and improve many previously known results for quasi-variational and variational inequality problems.

scholarly journals On completely generalized multi-valued co-variational inequalities involving strongly accretive operators

Filomat ◽  
2012 ◽  
Vol 26 (4) ◽  
pp. 657-663
Author(s):  
Rais Ahmad ◽  
Syed Irfan
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Banach Spaces ◽  
Iterative Algorithm ◽  
Variational Inequality Problem ◽  
Existence Of Solutions ◽  
Accretive Operators ◽  
Inequality Problem

In this paper we consider the completely generalized multi-valued co-variational inequality problem in Banach spaces and construct an iterative algorithm. We prove the existence of solutions for our problem involving strongly accretive operators and convergence of iterative sequences generated by the algorithm.

scholarly journals Existence theorems for vector variational inequalities

1996 ◽  
Vol 54 (3) ◽  
pp. 473-481 ◽  
Author(s):  
Aris Daniilidis ◽  
Nicolas Hadjisavvas
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Banach Spaces ◽  
Convex Subset ◽  
Variational Inequality Problem ◽  
Existence Of Solutions ◽  
Existence Theorems ◽  
Multivalued Operator ◽  
Inequality Problem ◽  
Vector Variational Inequality Problem

Given two real Banach spaces X and Y, a closed convex subset K in X, a cone with nonempty interior C in Y and a multivalued operator from K to 2L(x, y), we prove theorems concerning the existence of solutions for the corresponding vector variational inequality problem, that is the existence of some x0 ∈ K such that for every x ∈ K we have A(x − x0) ∉ − int C for some A ∈ Tx0. These results correct previously published ones.

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