Some existence theorems for generalized vector variational inequalities

  • Lee, Gue-Myung (Department of Natural Sciences, Pusan National University of Technology, Pusan 608-739) ;
  • Kim, Do-Sang (Department of Applied Mathematics, National Fisheries University of Pusan, Pusan 608-737) ;
  • Lee, Byung-Soo (Department of Mathematics, Kyungsung University, Pusan 608-736)
  • Published : 1995.08.01

Abstract

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 $C(x) \neq 0 and C(x) \neq Y$, where Int denotes the interior.