The Stability of Solution Set Mappings to Parametric Generalized Set-Valued Strong Equilibrium Problems
Ke Ke LI1,2, Zai Yun PENG3, Yong ZHAO3, Jing ZENG4
1. Department of Mathematics, Sichuan University, Chengdu 610064, P. R. China;
2. School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, P. R. China;
3. College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, P. R. China;
4. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, P. R. China
In this study, the lower semicontinuity of solution mappings to parametric generalized set-valued strong vector equilibrium problems is proved, by employing properties of the limit to set-valued mapping and the assumption of weakf-property, which method is different from the recent ones (Zhao, 2016 and Meng, 2018). Moreover, a sufficient condition of the solution sets to parametric generalized set-valued strong vector equilibrium problems is established, and examples are also given for the illustration of the correctness to the obtained results. The obtained results generalize and improve the ones in the literature (Gong, 2008, Xu, 2009, Chen, 2010, Xu, 2013 and Zhao, 2013).
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2019, Vol. 62 
