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Article Contents

# 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.
Mathematics Subject Classification: 90C31, 49J53.

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