Some existence theorems for generalized vector variational inequalities
Gue Myung Lee, Do Sang Kim, Byung Soo Lee · Bulletin of the Korean Mathematical Society · 1995
Let X and Y be two normed spaces and D a nonempty convex subset of X. Let $T : X to L(X,Y)$ be a mapping, where L(X,Y) is the space of all continuous linear mappings from X into Y. And let $C : D \to 2^Y$ be a set-valued map such that for each $x \in D$, C(x) is a convex cone in Y such that Int $C(x) eq 0 and C(x) eq Y$, where Int denotes the interior.