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Journal of Mathematics
Volume 2013, Article ID 204348, 6 pages
Research Article

Existence Results for Vector Mixed Quasi-Complementarity Problems

1Department of Mathematics, BITS-Pilani, Dubai Campus, P.O. Box 345055, Dubai, UAE
2Department of Mathematics, Al-Jouf University, P.O. Box 2014, Skaka, Saudi Arabia

Received 27 September 2012; Revised 16 January 2013; Accepted 17 January 2013

Academic Editor: Kaleem R. Kazmi

Copyright © 2013 Suhel Ahmad Khan and Naeem Ahmad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.