Journal of Inequalities and Applications
Volume 5 (2000), Issue 1, Pages 63-89
Generalized bi-quasi-variational inequalities for quasi-semi-monotone and bi-quasi-semi-monotone
operators with applications in non-compact settings and minimization problems
Department of Mathematics, The University of Queensland, Brisbane 4072, Queensland, Australia
Received 15 October 1998; Revised 10 May 1999
Copyright © 2000 Molhammad S. R. Chowdhury and E. Tarafdar. 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.
Results are obtained on existence theorems of generalized bi-quasi-variational inequalities for quasi-semi-monotone and bi-quasi-semi-monotone operators in both compact and non-compact settings. We shall use the concept of escaping sequences introduced by Border (Fixed Point Theorem with Applications to Economics and Game Theory, Cambridge University Press, Cambridge, 1985) to obtain results in non-compact settings. Existence theorems on non-compact generalized bi-complementarity problems for quasi-semi-monotone and bi-quasi-semi-monotone operators are also obtained. Moreover, as applications of some results of this paper on generalized bi-quasi-variational inequalities, we shall obtain existence of solutions for some kind of minimization problems with quasi-
semi-monotone and bi-quasi-semi-monotone operators.