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. 149, issue 3, No 8, 564-579

Abstract: Abstract In this paper, we study the solution stability of parametric weak Vector Variational Inequalities with set-valued and single-valued mappings, respectively. We obtain the lower semicontinuity of the solution mapping for the parametric set-valued weak Vector Variational Inequality with strictly C-pseudomapping in reflexive Banach spaces. Moreover, under some requirements that the mapping satisfies the degree conditions, we establish the lower semicontinuity of the solution mapping for a parametric single-valued weak Vector Variational Inequality in reflexive Banach spaces, by using the degree-theoretic approach. The results presented in this paper improve and extend some known results due to Kien and Yao (Set-Valued Anal. 16:399–412, 2008) and Wong (J. Glob. Optim. 46:435–446, 2010).

Keywords: Parametric weak Vector Variational Inequality; Strictly C-pseudomapping; Lower semicontinuity; Degree theory (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10957-011-9805-7

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