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LOWER SEMICONTINUITY OF PARAMETRIC GENERALIZED WEAK VECTOR EQUILIBRIUM PROBLEMS

  • SHENG-JIE LI (a1), HUI-MIN LIU (a2) and CHUN-RONG CHEN (a3)

Abstract

In this paper, using a scalarization method, we obtain sufficient conditions for the lower semicontinuity and continuity of the solution mapping to a parametric generalized weak vector equilibrium problem with set-valued mappings.

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Copyright

Corresponding author

For correspondence; e-mail: chencr1981@163.com

Footnotes

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This research was partially supported by the National Natural Science Foundation of China (Grant number: 10871216).

Footnotes

References

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[1]Anh, L. Q. and Khanh, P. Q., ‘Semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems’, J. Math. Anal. Appl. 294 (2004), 699711.
[2]Anh, L. Q. and Khanh, P. Q., ‘On the stability of the solution sets of general multivalued vector quasiequilibrium problems’, J. Optim. Theory Appl. 135 (2007), 271284.
[3]Aubin, J. P. and Ekeland, I., Applied Nonlinear Analysis (John Wiley and Sons, New York, 1984).
[4]Berge, C., Topological Spaces (Oliver and Boyd, London, 1963).
[5]Chen, G. Y., Huang, X. X. and Yang, X. Q., Vector Optimization: Set-valued and Variational Analysis (Springer, Berlin, 2005).
[6]Chen, C. R. and Li, S. J., ‘Semicontinuity of the solution set map to a set-valued weak vector variational inequality’, J. Ind. Manag. Optim. 3 (2007), 519528.
[7]Chen, C. R., Li, S. J. and Teo, K. L., ‘Solution semicontinuity of parametric generalized vector equilibrium problems’, J. Global Optim. 45 (2009), 309318.
[8]Cheng, Y. H. and Zhu, D. L., ‘Global stability results for the weak vector variational inequality’, J. Global Optim. 32 (2005), 543550.
[9]Ferro, F., ‘A minimax theorem for vector-valued functions’, J. Optim. Theory Appl. 60 (1989), 1931.
[10]Giannessi (ed.), F., Vector Variational Inequalities and Vector Equilibria: Mathematical Theories (Kluwer, Dordrecht, 2000).
[11]Gong, X. H., ‘Continuity of the solution set to parametric weak vector equilibrium problems’, J. Optim. Theory Appl. 139 (2008), 3546.
[12]Gong, X. H. and Yao, J. C., ‘Lower semicontinuity of the set of efficient solutions for generalized systems’, J. Optim. Theory Appl. 138 (2008), 197205.
[13]Huang, N. J., Li, J. and Thompson, H. B., ‘Stability for parametric implicit vector equilibrium problems’, Math. Comput. Modelling 43 (2006), 12671274.
[14]Jahn, J., Vector Optimization—Theory, Applications and Extensions (Springer, Berlin, 2004).
[15]Khanh, P. Q. and Luu, L. M., ‘Upper semicontinuity of the solution set to parametric vector quasivariational inequalities’, J. Global Optim. 32 (2005), 569580.
[16]Kimura, K. and Yao, J. C., ‘Semicontinuity of solution mappings of parametric generalized vector equilibrium problems’, J. Optim. Theory Appl. 138 (2008), 429443.
[17]Kimura, K. and Yao, J. C., ‘Sensitivity analysis of solution mappings of parametric vector quasi-equilibrium problems’, J. Global Optim. 41 (2008), 187202.
[18]Li, S. J. and Chen, C. R., ‘Stability of weak vector variational inequality’, Nonlinear Anal. 70 (2009), 15281535.
[19]Li, S. J., Chen, G. Y. and Teo, K. L., ‘On the stability of generalized vector quasivariational inequality problems’, J. Optim. Theory Appl. 113 (2002), 283295.
[20]Li, S. J. and Fang, Z. M., ‘On the stability of a dual weak vector variational inequality problem’, J. Ind. Manag. Optim. 4 (2008), 155165.
[21]Li, J. and Huang, N. J., ‘Implicit vector equilibrium problems via nonlinear scalarization’, Bull. Austral. Math. Soc. 72 (2005), 161172.
[22]Song, W., ‘Vector equilibrium problems with set-valued mappings’, in: Vector Variational Inequalities and Vector Equilibria: Mathematical Theories (ed. Giannessi, F.) (Kluwer, Dordrecht, 2000), pp. 403422.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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