摘要
Let E,F be topological vector spaces over the field Phi (which is either the real field R or the complex field C), let (,): F x E --> Phi be a bilinear functional, and let X be a nonempty subset of E. Given a multi-valued map S:X --> 2x, two multi-valued maps M,T:X --> 2F and a function h:X x X --> R, the generalized bi-quasi-variational inequality problem (GBQVIP) is to find a point y is-an-element-of X such that y is-an-element-of S(y) and inf Re(f - w,y - x) + h(y,x) less-than-or-equal-to 0 for all x is-an-element-of S(y) and for all f is-an-element-of M(y). In this paper, we obtain three general existence theorems on solutions of GBQVIPs which simultaneously unify, sharpen and extend the corresponding results of Shih-Tan and Zhou-Chen to paracompact setting.
Let E,F be topological vector spaces over the field Phi (which is either the real field R or the complex field C), let (,): F x E --> Phi be a bilinear functional, and let X be a nonempty subset of E. Given a multi-valued map S:X --> 2x, two multi-valued maps M,T:X --> 2F and a function h:X x X --> R, the generalized bi-quasi-variational inequality problem (GBQVIP) is to find a point y is-an-element-of X such that y is-an-element-of S(y) and inf Re(f - w,y - x) + h(y,x) less-than-or-equal-to 0 for all x is-an-element-of S(y) and for all f is-an-element-of M(y). In this paper, we obtain three general existence theorems on solutions of GBQVIPs which simultaneously unify, sharpen and extend the corresponding results of Shih-Tan and Zhou-Chen to paracompact setting.
