On the solution existence of generalized quasivariational inequalities with discontinuous multifunctions
https://doi.org/10.1007/s10957-007-9239-4Publisher, magazine: ,
Publication year: 2007
Lưu Trích dẫn Chia sẻAbstract
We study the following generalized quasivariational inequality problem: given a closed convex set X in a normed space E with the dual E *, a multifunction Φ:X→2E∗ and a multifunction Γ:X→2X, find a point (x^,z^)∈X×E∗ such that x^∈Γ(x^),z^∈Φ(x^),⟨z^,x^−y⟩≤0 , ∀y∈Γ(x^) . We prove some existence theorems in which Φ may be discontinuous, X may be unbounded, and Γ is not assumed to be Hausdorff lower semicontinuous.
Tags: Generalized quasivariational inequalities, Lower semicontinuity, Hausdorff upper semicontinuity, Hausdorff lower semicontinuity, Multifunctions, Closed graphs, Open graphs.
Các bài viết liên quan đến tác giả Bùi Trọng Kiên
On the metric projection onto a family of closed convex sets in a uniformly convex Banach space
Covering properties at positive-order rates of multifunctions and some related topics
Generalized vector variational inequalities with star-pseudomonotone and discontinuous operators
On the solution existence of pseudomonotone variational inequalities
On the lower semicontinuity of optimal solution sets
Solution sensitivity of a generalized variational inequality