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Semicontinuity of the solution set map to a set-valued weak vector variational inequality
This paper investigates the semicontinuity of the solution set map
for a parametric set-valued weak vector variational inequality in
Banach spaces. The upper semicontinuity and closedness of the
solution set map are obtained. A parametric gap function is
proposed by using a nonlinear scalarization function. By virtue of
the parametric gap function and a key assumption, the lower
semicontinuity of the solution set map is established.