Stability analysis for Minty mixed variational inequality in reflexive Banach spaces. (English) Zbl 1218.49032
Summary: This paper is devoted to the stability analysis for a class of Minty mixed variational inequalities in reflexive Banach spaces, when both the mapping and the constraint set are perturbed. Several equivalent characterizations are given for the Minty mixed variational inequality to have a nonempty and bounded solution set. A stability result is presented for the Minty mixed variational inequality with \(\Phi\)-pseudomonotone mapping in reflexive Banach space, when both the mapping and the constraint set are perturbed by different parameters. As an application, a stability result for a generalized mixed variational inequality is also obtained. The results presented in this paper generalize and extend some known results in J. Fan and R. Zhong [Nonlinear Anal., Theory Methods Appl. 69, No. 8, A, 2566–2574 (2008; Zbl 1172.49010)] and Y. He [J. Math. Anal. Appl. 330, No. 1, 352–363 (2007; Zbl 1124.49005)].
MSC:
| 49K40 | Sensitivity, stability, well-posedness |
| 90C31 | Sensitivity, stability, parametric optimization |
| 49J40 | Variational inequalities |
Keywords:
mixed variational inequality; stability; recession cone; recession function; barrier cone; pseudomonotone mappingReferences:
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