Continuity of the solution set mappings for parametric unified weak quasivariational inequalities via free-disposal set mappings. (English) Zbl 1447.49023
Summary: In this study, we mainly study the stability for a parametric unified weak quasivariational inequality (PUWQVI) under free-disposal set mappings. Firstly, by using a nonlinear scalarization method, we establish the semicontinuity of gap functions and solution mappings for (PUWQVI). Then, under the free-disposal set mapping assumption, we obtain some sufficient conditions of the outer-continuity and the outer-openness for (PUWQVI), and the inner-openness for parametric unified set-valued strong vector quasivariational inequalities, respectively. Moreover, examples are given to illustrate our results; our results are new and improve the corresponding ones in the literature.
MSC:
| 49J45 | Methods involving semicontinuity and convergence; relaxation |
| 49J40 | Variational inequalities |
Keywords:
free-disposal set mapping; nonlinear scalarization; lower semicontinuity; out/inner-continuity; out-opennessReferences:
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