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October  2014, 10(4): 1225-1234. doi: 10.3934/jimo.2014.10.1225

Lower semicontinuity of the solution mapping to a parametric generalized vector equilibrium problem

 1 College of Sciences, Chongqing Jiaotong University, Chongqing, 400074 2 College of Mathematics and Statistics, Chongqing University, Chongqing, 401331

Received  March 2013 Revised  September 2013 Published  February 2014

This paper deals with the lower semicontinuity of the solution mapping to a parametric generalized vector equilibrium problem. Under new assumptions, which do not contain any information about solution mappings, we establish the lower semicontinuity of the solution mapping to a parametric generalized vector equilibrium problem by using a scalarization method. These results improve the corresponding ones in recent literature. Some examples are given to illustrate our results.
Citation: Qilin Wang, Shengji Li. Lower semicontinuity of the solution mapping to a parametric generalized vector equilibrium problem. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1225-1234. doi: 10.3934/jimo.2014.10.1225
References:

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References:
 [1] Kenji Kimura, Jen-Chih Yao. Semicontinuity of solution mappings of parametric generalized strong vector equilibrium problems. Journal of Industrial & Management Optimization, 2008, 4 (1) : 167-181. doi: 10.3934/jimo.2008.4.167 [2] Qilin Wang, Shengji Li. Semicontinuity of approximate solution mappings to generalized vector equilibrium problems. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1303-1309. doi: 10.3934/jimo.2016.12.1303 [3] Xin Zuo, Chun-Rong Chen, Hong-Zhi Wei. Solution continuity of parametric generalized vector equilibrium problems with strictly pseudomonotone mappings. Journal of Industrial & Management Optimization, 2017, 13 (1) : 477-488. doi: 10.3934/jimo.2016027 [4] Qiusheng Qiu, Xinmin Yang. Scalarization of approximate solution for vector equilibrium problems. Journal of Industrial & Management Optimization, 2013, 9 (1) : 143-151. doi: 10.3934/jimo.2013.9.143 [5] Xiao-Bing Li, Xian-Jun Long, Zhi Lin. Stability of solution mapping for parametric symmetric vector equilibrium problems. Journal of Industrial & Management Optimization, 2015, 11 (2) : 661-671. doi: 10.3934/jimo.2015.11.661 [6] Nguyen Ba Minh, Pham Huu Sach. Strong vector equilibrium problems with LSC approximate solution mappings. Journal of Industrial & Management Optimization, 2020, 16 (2) : 511-529. doi: 10.3934/jimo.2018165 [7] Yangdong Xu, Shengjie Li. Continuity of the solution mappings to parametric generalized non-weak vector Ky Fan inequalities. Journal of Industrial & Management Optimization, 2017, 13 (2) : 967-975. doi: 10.3934/jimo.2016056 [8] Lam Quoc Anh, Nguyen Van Hung. Gap functions and Hausdorff continuity of solution mappings to parametric strong vector quasiequilibrium problems. Journal of Industrial & Management Optimization, 2018, 14 (1) : 65-79. doi: 10.3934/jimo.2017037 [9] Kenji Kimura, Yeong-Cheng Liou, Soon-Yi Wu, Jen-Chih Yao. Well-posedness for parametric vector equilibrium problems with applications. Journal of Industrial & Management Optimization, 2008, 4 (2) : 313-327. doi: 10.3934/jimo.2008.4.313 [10] Lam Quoc Anh, Pham Thanh Duoc, Tran Ngoc Tam. Continuity of approximate solution maps to vector equilibrium problems. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1685-1699. doi: 10.3934/jimo.2017013 [11] Chunrong Chen, Zhimiao Fang. A note on semicontinuity to a parametric generalized Ky Fan inequality. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 779-784. doi: 10.3934/naco.2012.2.779 [12] Zaiyun Peng, Xinmin Yang, Kok Lay Teo. On the Hölder continuity of approximate solution mappings to parametric weak generalized Ky Fan Inequality. Journal of Industrial & Management Optimization, 2015, 11 (2) : 549-562. doi: 10.3934/jimo.2015.11.549 [13] Jiawei Chen, Guangmin Wang, Xiaoqing Ou, Wenyan Zhang. Continuity of solutions mappings of parametric set optimization problems. Journal of Industrial & Management Optimization, 2020, 16 (1) : 25-36. doi: 10.3934/jimo.2018138 [14] Yu Han, Nan-Jing Huang. Some characterizations of the approximate solutions to generalized vector equilibrium problems. Journal of Industrial & Management Optimization, 2016, 12 (3) : 1135-1151. doi: 10.3934/jimo.2016.12.1135 [15] Kenji Kimura, Yeong-Cheng Liou, David S. Shyu, Jen-Chih Yao. Simultaneous system of vector equilibrium problems. Journal of Industrial & Management Optimization, 2009, 5 (1) : 161-174. doi: 10.3934/jimo.2009.5.161 [16] M. H. Li, S. J. Li, W. Y. Zhang. Levitin-Polyak well-posedness of generalized vector quasi-equilibrium problems. Journal of Industrial & Management Optimization, 2009, 5 (4) : 683-696. doi: 10.3934/jimo.2009.5.683 [17] Jingjing Wang, Zaiyun Peng, Zhi Lin, Daqiong Zhou. On the stability of solutions for the generalized vector quasi-equilibrium problems via free-disposal set. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020002 [18] Shengji Li, Xiaole Guo. Calculus rules of generalized $\epsilon-$subdifferential for vector valued mappings and applications. Journal of Industrial & Management Optimization, 2012, 8 (2) : 411-427. doi: 10.3934/jimo.2012.8.411 [19] Hong-Zhi Wei, Xin Zuo, Chun-Rong Chen. Unified vector quasiequilibrium problems via improvement sets and nonlinear scalarization with stability analysis. Numerical Algebra, Control & Optimization, 2020, 10 (1) : 107-125. doi: 10.3934/naco.2019036 [20] Adela Capătă. Optimality conditions for vector equilibrium problems and their applications. Journal of Industrial & Management Optimization, 2013, 9 (3) : 659-669. doi: 10.3934/jimo.2013.9.659

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