Characterizations of weakly sharp solutions for a variational inequality with a pseudomonotone mapping

For a variational inequality problem with a pseudomonotone mapping F, we characterize the weak sharpness of its solution set 0 without using gap functions. When the mapping F is also constant on 0, the characterizations of weak sharpness of C* become more succinct. As an example, a pseudomonotone(+) mapping on 0 is shown to be constant on C*. Consequently the weak sharpness of C* can further be described by a Gateaux differentiable function which itself characterizes the pseudomonotonicity(+) of F on C*. It turns out that several existing relevant results with differentiable gap functions can be obtained from ours. (C) 2017 Elsevier B.V. All rights reserved.