Continuity of the solution set mappings for parametric unified weak quasivariational inequalities via free-disposal set mappings. (1st September 2020) - Li, Ke-Ke; Peng, Zai-Yun; Lin, Zhi; Long, Xian-Jun
ABSTRACT: In this study, we mainly study the stability for 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 inequality, respectively. Moreover, examples are given to illustrate our results, our results are new and improve the corresponding ones in the literature.