Semicontinuity of the solution set map to a set-valued weak vector variational inequality

C. R. Chen; S. J. Li

doi:10.3934/jimo.2007.3.519

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2007, Volume 3, Issue 3: 519-528. Doi: 10.3934/jimo.2007.3.519

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Semicontinuity of the solution set map to a set-valued weak vector variational inequality

C. R. Chen^1, and
S. J. Li^1,

1.
College of Mathematics and Science, Chongqing University, Chongqing, 400044

Received: August 31, 2006

Revised: November 30, 2006

Published: June 2007

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Abstract

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.

Keywords:

Lower semicontinuity,
upper semicontinuity,
nonlinear scalarization function,
parametric gap function,
set-valued weak vector variational inequality.

Mathematics Subject Classification: 90C31, 49J53.

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