Lower Semicontinuity for Parametric Weak Vector Variational Inequalities in Reflexive Banach Spaces

Ren-you Zhong and Nan-jing Huang ()
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Ren-you Zhong: Sichuan University
Nan-jing Huang: Sichuan University

Journal of Optimization Theory and Applications, 2011, vol. 150, issue 2, No 7, 317-326

Abstract: Abstract In this paper, a key assumption similar to that of Li and Chen is introduced by virtue of a gap function for a class of parametric set-valued weak vector variational inequalities in Banach spaces. By using this key assumption, sufficient and necessary conditions of the continuity and Hausdorff continuity of the solution set mapping for such parametric set-valued weak vector variational inequalities are given in Banach spaces when the image space is infinite dimensional. The results presented in this paper generalize and improve some main results of Li and Chen.

Keywords: Hausdorff lower semicontinuity; Hausdorff continuity; Set-valued mapping; Parametric gap function; Weak vector variational inequality (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10957-011-9843-1

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