Mohammad S.R. Chowdhury, Sharafat Ali
Department of Mathematics
Lahore University of Management Sciences (LUMS)
Opposite Sector U, D.H.A, Lahore Cantt.
Lahore, 54792, PAKISTAN
Department of Mathematics
International Islamic University (IIU)
Islamabad, Sector H-10, PAKISTAN

Abstract.In this paper, the authors prove some existence results of solutions for a new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo-monotone type I operators in non-compact settings in locally convex Hausdorff topological vector spaces.

In obtaining these results on GBQVI for quasi-pseudo-monotone type I operators in non-compact settings, we shall use the concept of escaping sequences introduced by Border [2] by applying Chowdhury and Tan's result on generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type I operators on compact sets [11]. As an application, an existence theorem on generalized bi-complementarity problem for quasi-pseudo-monotone type I operators is given in non-compact settings.

Received: August 14, 2008

AMS Subject Classification: 47H05

Key Words and Phrases: generalized bi-quasi-variational inequalities, quasi-pseudomonotone type I operators, escaping sequences, locally convex Hausdorff topological vector spaces, cone, dual cone, bilinear functional, generalized bi-complementarity problems

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 49
Issue: 3