Generalized Quasi-variational Inequalities in Locally Convex Topological Vector Spaces
Ding Xie-ping · Journal of Sichuan Normal University · 2002
Let X be a paracompact convex subset of a locally convex space E, F:X→2 X be a set-valued mapping and φ:X×X→R be a real function. We study the following abstract generalized quasi-variational inequality (AGQVI): finding ∈X such that ∈F() and φ(,y)0, y∈F(), where the φ(x,y) is 0-transfer compactly lower semicontinuous in x and 0-diagonally quasi-concave in y. Applying this result, we obtain some generalizations of many known results for generalized quasi-variational inequalities in recent literature.