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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:
[1]

J. Math. Anal. Appl., 294 (2004), 699-711. doi: 10.1016/j.jmaa.2004.03.014.  Google Scholar

[2]

J. Optim. Theory Appl., 135 (2007), 271-284. doi: 10.1007/s10957-007-9250-9.  Google Scholar

[3]

Wiley, New York, 1984.  Google Scholar

[4]

Oliver and Boyd, London, 1963. Google Scholar

[5]

J. Optim. Theory Appl., 92 (1997), 527-542. doi: 10.1023/A:1022603406244.  Google Scholar

[6]

J. Ind. Manag. Optim., 3 (2007), 519-528. doi: 10.3934/jimo.2007.3.519.  Google Scholar

[7]

J. Glob. Optim., 45 (2009), 309-318. doi: 10.1007/s10898-008-9376-9.  Google Scholar

[8]

Pac. J. Optim., 6 (2010), 141-151.  Google Scholar

[9]

J. Glob. Optim., 32 (2005), 543-550. doi: 10.1007/s10898-004-2692-9.  Google Scholar

[10]

J. Optim. Theory Appl., 60(1989), 19-31. doi: 10.1007/BF00938796.  Google Scholar

[11]

J. Glob. Optim., 31(2005), 109-119. doi: 10.1007/s10898-004-4274-2.  Google Scholar

[12]

Kluwer Academic Publishers, Dordrecht, 2000. doi: 10.1007/978-1-4613-0299-5.  Google Scholar

[13]

J. Optim. Theory Appl., 133 (2007), 151-161. doi: 10.1007/s10957-007-9196-y.  Google Scholar

[14]

J. Optim. Theory Appl., 138(2008), 197-205. doi: 10.1007/s10957-008-9379-1.  Google Scholar

[15]

J. Optim. Theory Appl., 139(2008), 35-46. doi: 10.1007/s10957-008-9429-8.  Google Scholar

[16]

J. Optim. Theory Appl., 138 (2008), 189-196. doi: 10.1007/s10957-008-9378-2.  Google Scholar

[17]

Math. Comput. Model., 43 (2006), 1267-1274. doi: 10.1016/j.mcm.2005.06.010.  Google Scholar

[18]

Optimization, 54 (2005), 123-130. doi: 10.1080/02331930412331330379.  Google Scholar

[19]

J. Glob. Optim., 41 (2008), 187-202. doi: 10.1007/s10898-007-9210-9.  Google Scholar

[20]

J. Ind. Manag. Optim., 4 (2008), 167-181. doi: 10.3934/jimo.2008.4.167.  Google Scholar

[21]

Taiwanese J. Math., 12 (2008), 2233-2268.  Google Scholar

[22]

Taiwanese J. Math., 12 (2008), 649-669.  Google Scholar

[23]

J. Optim. Theory Appl., 133 (2007), 329-339. doi: 10.1007/s10957-007-9190-4.  Google Scholar

[24]

J. Math. Anal. Appl., 215 (1997), 297-316. doi: 10.1006/jmaa.1997.5568.  Google Scholar

[25]

J. Optim. Theory Appl., 83 (1994), 63-81. doi: 10.1007/BF02191762.  Google Scholar

[26]

J. Optim. Theory Appl., 113 (2002), 297-323. doi: 10.1023/A:1014830925232.  Google Scholar

[27]

J. Ind. Manag. Optim.,, 4 (2008), 155-165. doi: 10.3934/jimo.2008.4.155.  Google Scholar

[28]

Nonlinear Anal., 70 (2009), 1528-1535. doi: 10.1016/j.na.2008.02.032.  Google Scholar

[29]

J. Optim. Theory Appl., 147 (2010), 507-515. doi: 10.1007/s10957-010-9736-8.  Google Scholar

[30]

Bull. Aust. Math. Soc., 81 (2010), 85-95. doi: 10.1017/S0004972709000628.  Google Scholar

[31]

J. Glob. Optim., 55 (2013), 597-610. doi: 10.1007/s10898-012-9985-1.  Google Scholar

[32]

Positivity, 17 (2013), 341-353. doi: 10.1007/s11117-012-0170-z.  Google Scholar

[33]

J. Optim. Theory Appl., 110 (2001), 413-427. doi: 10.1023/A:1017535631418.  Google Scholar

show all references

References:
[1]

J. Math. Anal. Appl., 294 (2004), 699-711. doi: 10.1016/j.jmaa.2004.03.014.  Google Scholar

[2]

J. Optim. Theory Appl., 135 (2007), 271-284. doi: 10.1007/s10957-007-9250-9.  Google Scholar

[3]

Wiley, New York, 1984.  Google Scholar

[4]

Oliver and Boyd, London, 1963. Google Scholar

[5]

J. Optim. Theory Appl., 92 (1997), 527-542. doi: 10.1023/A:1022603406244.  Google Scholar

[6]

J. Ind. Manag. Optim., 3 (2007), 519-528. doi: 10.3934/jimo.2007.3.519.  Google Scholar

[7]

J. Glob. Optim., 45 (2009), 309-318. doi: 10.1007/s10898-008-9376-9.  Google Scholar

[8]

Pac. J. Optim., 6 (2010), 141-151.  Google Scholar

[9]

J. Glob. Optim., 32 (2005), 543-550. doi: 10.1007/s10898-004-2692-9.  Google Scholar

[10]

J. Optim. Theory Appl., 60(1989), 19-31. doi: 10.1007/BF00938796.  Google Scholar

[11]

J. Glob. Optim., 31(2005), 109-119. doi: 10.1007/s10898-004-4274-2.  Google Scholar

[12]

Kluwer Academic Publishers, Dordrecht, 2000. doi: 10.1007/978-1-4613-0299-5.  Google Scholar

[13]

J. Optim. Theory Appl., 133 (2007), 151-161. doi: 10.1007/s10957-007-9196-y.  Google Scholar

[14]

J. Optim. Theory Appl., 138(2008), 197-205. doi: 10.1007/s10957-008-9379-1.  Google Scholar

[15]

J. Optim. Theory Appl., 139(2008), 35-46. doi: 10.1007/s10957-008-9429-8.  Google Scholar

[16]

J. Optim. Theory Appl., 138 (2008), 189-196. doi: 10.1007/s10957-008-9378-2.  Google Scholar

[17]

Math. Comput. Model., 43 (2006), 1267-1274. doi: 10.1016/j.mcm.2005.06.010.  Google Scholar

[18]

Optimization, 54 (2005), 123-130. doi: 10.1080/02331930412331330379.  Google Scholar

[19]

J. Glob. Optim., 41 (2008), 187-202. doi: 10.1007/s10898-007-9210-9.  Google Scholar

[20]

J. Ind. Manag. Optim., 4 (2008), 167-181. doi: 10.3934/jimo.2008.4.167.  Google Scholar

[21]

Taiwanese J. Math., 12 (2008), 2233-2268.  Google Scholar

[22]

Taiwanese J. Math., 12 (2008), 649-669.  Google Scholar

[23]

J. Optim. Theory Appl., 133 (2007), 329-339. doi: 10.1007/s10957-007-9190-4.  Google Scholar

[24]

J. Math. Anal. Appl., 215 (1997), 297-316. doi: 10.1006/jmaa.1997.5568.  Google Scholar

[25]

J. Optim. Theory Appl., 83 (1994), 63-81. doi: 10.1007/BF02191762.  Google Scholar

[26]

J. Optim. Theory Appl., 113 (2002), 297-323. doi: 10.1023/A:1014830925232.  Google Scholar

[27]

J. Ind. Manag. Optim.,, 4 (2008), 155-165. doi: 10.3934/jimo.2008.4.155.  Google Scholar

[28]

Nonlinear Anal., 70 (2009), 1528-1535. doi: 10.1016/j.na.2008.02.032.  Google Scholar

[29]

J. Optim. Theory Appl., 147 (2010), 507-515. doi: 10.1007/s10957-010-9736-8.  Google Scholar

[30]

Bull. Aust. Math. Soc., 81 (2010), 85-95. doi: 10.1017/S0004972709000628.  Google Scholar

[31]

J. Glob. Optim., 55 (2013), 597-610. doi: 10.1007/s10898-012-9985-1.  Google Scholar

[32]

Positivity, 17 (2013), 341-353. doi: 10.1007/s11117-012-0170-z.  Google Scholar

[33]

J. Optim. Theory Appl., 110 (2001), 413-427. doi: 10.1023/A:1017535631418.  Google Scholar

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