Stability analysis for set-valued vector mixed variational inequalities in real reflexive Banach spaces

Xing Wang; Nan-Jing Huang

doi:10.3934/jimo.2013.9.57

Article Contents

2013, Volume 9, Issue 1: 57-74. Doi: 10.3934/jimo.2013.9.57

This issue Previous Article Production-distribution planning of construction supply chain management under fuzzy random environment for large-scale construction projects Next Article A class of nonlinear Lagrangian algorithms for minimax problems

Stability analysis for set-valued vector mixed variational inequalities in real reflexive Banach spaces

Xing Wang^1, and
Nan-Jing Huang^2,

1.
Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064
2.
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064

Received: October 31, 2011

Revised: April 30, 2012

Published: December 2012

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Abstract

In this paper, some characterizations for the solution sets of a class of set-valued vector mixed variational inequalities to be nonempty and bounded are presented in real reflexive Banach spaces. An equivalence relation between the solution sets of the vector mixed variational inequalities and the weakly efficient solution sets of the vector optimization problems is shown under some suitable assumptions. By using some known results for the vector optimization problems, several characterizations for the solution sets of the vector mixed variational inequalities are obtained in real reflexive Banach spaces. Furthermore, some stability results for the vector mixed variational inequality are given when the mapping and the constraint set are perturbed by two different parameters. Finally, the upper semicontinuity and the lower semicontinuity of the solution sets are given under some suitable assumptions which are different from the ones used in [7, 11, 22]. Some examples are also given to illustrate our results.

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Mathematics Subject Classification: 49J40.

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