Fixed Point Theory and Applications
Volume 2005 (2005), Issue 3, Pages 243-255

On generalized vector quasivariational-like inequality problems

Abdul Khaliq1,2 and Mohammad Rashid1,3

1Post Graduate Department of Mathematics, University of Jammu, Jammu and Kashmir 180006, India
2Post Graduate Department of Applied Mathematics, BGSB University, Rajouri, Jammu and Kashmir 185131, India
3Department of Mathematics, Government Degree College, Rajouri, Jammu and Kashmir 185131, India

Received 6 September 2004; Revised 3 July 2005

Copyright © 2005 Abdul Khaliq and Mohammad Rashid. 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 a class of generalized vector quasivariational-like inequality problems in Banach spaces. We derive some new existence results by using KKM-Fan theorem and an equivalent fixed point theorem. As an application of our results, we have obtained as special cases the existence results for vector quasi-equilibrium problems, generalized vector quasivariational inequality and vector quasi-optimization problems. The results of this paper generalize and unify the corresponding results of several authors and can be considered as a significant extension of the previously known results.