Skip to main content Accessibility help
×
Home
Hostname: page-component-cf9d5c678-vbn2q Total loading time: 0.193 Render date: 2021-07-28T17:23:32.906Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

GENERALIZED MIXED QUASI-COMPLEMENTARITY PROBLEMS IN TOPOLOGICAL VECTOR SPACES

Published online by Cambridge University Press:  01 April 2008

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)
Corresponding
Rights & Permissions[Opens in a new window]

Abstract

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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2008

References

[1]Aslam Noor, M., “Mixed quasi variational inequalities”, Appl. Math. Comput. 146 (2003) 553578.Google Scholar
[2]Aslam Noor, M., “Fundamentals of mixed quasi variational inequalities”, Int. J. Pure Appl. Math. 15 (2004) 138257.Google Scholar
[3]Aslam Noor, M., “Some developments in general variational inequalities”, Appl. Math. Comput. 152 (2004) 199277.Google Scholar
[4]Aslam Noor, M., Inayat Noor, K. and Rassias, Th. M., “Some aspects of variational inequalities”, J. Comput. Appl. Math. 47 (1993) 285312.CrossRefGoogle Scholar
[5]Baiochhi, C. and Capelo, A., Variational and quasivariational inequalities (John Wiley and Sons, New York, 1984).Google Scholar
[6]Blum, E. and Oettli, W., “From optimization and variational inequalities to equilibrium problems”, Math. Stud. 63 (1994) 123145.Google Scholar
[7]Bnouhachem, A. and Aslam Noor, M., “A new predictor-corrector method for pseudomonotone nonlinear complementarity problem”, Int. J. Comput. Math. (2007) in press.Google Scholar
[8]Cho, Y. J., Li, J. and Huang, N. J., “Solvability of implicit complementarity problems”, Math. Comput. Modelling 45 (2007) 10011009.CrossRefGoogle Scholar
[9]Cottle, R. W., “Complementarity and variational problems”, Sympos. Math. 19 (1976) 177208.Google Scholar
[10]Cottle, R. W. and Dantzig, G. B., “Complementarity pivot theory of mathematical programming”, Linear Algebra. Appl. 1 (1968) 163185.CrossRefGoogle Scholar
[11]Fakhar, M. and Zafarani, J., “Generalized vector equilibrium problems for pseudomonotone multivalued bifunctions”, J. Optim. Theory Appl. 126 (2005) 109124.CrossRefGoogle Scholar
[12]Farajzadeh, A. P., Amini-Harandi, A. and Aslam Noor, M., “On the generalized vectorF-implicit complementarity problems and vector F-implicit variational inequality problems”, Math. Commun. (2007) in press.Google Scholar
[13]Glowinski, R., Lions, J. L. and Tremolieres, R., Numerical analysis of variational inequalities (North-Holland, Amsterdam, 1981).Google Scholar
[14]Huang, N. J., Li, J. and O’Regan, D., “Generalized f-complementarity problems in Banch Spaces”, Nonlinear Anal. (2007) doi.10.1016/j.na.2007.04.022.Google Scholar
[15]Inoan, D. and Kolumban, J., “On pseudomonotone set-valued mappings”, Nonlinear Anal. (2007) in press.Google Scholar
[16]Itoh, S., Takahashi, W. and Yanagi, K., “Variational inequalities and complementarity problems”, J. Math. Soc. Japan 30 (1978) 2328.CrossRefGoogle Scholar
[17]Karamardian, S., “Generalized complementarity problems”, J. Optim. Theory Appl. 8 (1971) 223239.CrossRefGoogle Scholar
[18]Lemke, C. E., “Bimatrix equilibrium point and mathematical programming”, Manag. Sci. 11 (1965) 681689.CrossRefGoogle Scholar
[19]Mosco, U., “Implicit variational problems and quasi variational inequalities”, in Nonlinear operators and the calculus of variations, Volume 543 of Lect. Notes Math. (Springer, Berlin, 1976) 83156.CrossRefGoogle Scholar
You have Access

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

GENERALIZED MIXED QUASI-COMPLEMENTARITY PROBLEMS IN TOPOLOGICAL VECTOR SPACES
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

GENERALIZED MIXED QUASI-COMPLEMENTARITY PROBLEMS IN TOPOLOGICAL VECTOR SPACES
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

GENERALIZED MIXED QUASI-COMPLEMENTARITY PROBLEMS IN TOPOLOGICAL VECTOR SPACES
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *