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GENERALIZED MIXED QUASI-COMPLEMENTARITY PROBLEMS IN TOPOLOGICAL VECTOR SPACES

Part of: Existence theories

Published online by Cambridge University Press:  01 April 2008

ALI P. FRAJZADEH  and
MUHAMMAD ASLAM NOOR
ALI P. FRAJZADEH*
Affiliation:
Mathematics Department, Razi University, Kermanshah, 67149, Iran (email: ali-ff@sci.razi.ac.ir)
MUHAMMAD ASLAM NOOR
Affiliation:
Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan (email: noormaslam@hotmail.com)
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Abstract

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In this paper, we introduce and consider a new class of complementarity problems, which are called the generalized mixed quasi-complementarity problems in a topological vector space. We show that the generalized mixed quasi-complementarity problems are equivalent to the generalized mixed quasi variational inequalities. Using a new type of KKM mapping theorem, we study the existence of a solution of the generalized mixed quasi-variational inequalities and generalized mixed quasi-complementarity problems. Several special cases are also discussed. The results obtained in this paper can be viewed as extension and generalization of the previously known results.

Keywords

complementarity problemsvariational inequalitiesexistence results

MSC classification

Secondary: 49J40: Variational methods including variational inequalities 90C33: Complementarity and equilibrium problems and variational inequalities (finite dimensions)
Type
Research Article
Information
The ANZIAM Journal , Volume 49 , Issue 4 , April 2008 , pp. 525 - 531
Copyright
Copyright © Australian Mathematical Society 2008

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