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Gap Functions and Existence of Solutions to Generalized Vector Quasi-Equilibrium Problems

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Abstract

This paper deals with generalized vector quasi-equilibrium problems. By virtue of a nonlinear scalarization function, the gap functions for two classes of generalized vector quasi-equilibrium problems are obtained. Then, from an existence theorem for a generalized quasi-equilibrium problem and a minimax inequality, existence theorems for two classes of generalized vector quasi-equilibrium problems are established.

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References

  1. Q.H. Ansari Fabian Flores-Bazan (2003) ArticleTitleGeneralized vector quasi-equilibrium problems with applications Journal of Mathematical Analysis and Applications 277 246–256 Occurrence Handle10.1016/S0022-247X(02)00535-8

    Article  Google Scholar 

  2. J.P. Aubin I. Ekeland (1984) Applied Nonlinear Analysis John Wiley and Sons New York

    Google Scholar 

  3. G.Y. Chen C.J. Goh X.Q. Yang (1999) ArticleTitleVector network equilibrium problems and nonlinear scalarization methods Mathematical Methods of Operation Research 49 239–253

    Google Scholar 

  4. G.Y. Chen C.J. Goh X.Q. Yang (2000) On gap functions for vector variational inequalities F. Giannessi (Eds) Vector Variational Inequalities and Vector Equilibria Kluwer Academic Publishers Dordrecht, Holland 55–72

    Google Scholar 

  5. Chen, G.Y., Yang, X.Q. and Yu, H. (2004), A nonlinear scalarization function and generalized quasi-vector equilibrium problems, Journal of Global Optimization. In press, available online.

  6. C. Gerth P. Weidner (1990) ArticleTitleNonconvex separation theorems and some applications in vector optimization Journal of Optimization Theory and Applications 67 297–320 Occurrence Handle10.1007/BF00940478

    Article  Google Scholar 

  7. C.W. Ha (1980) ArticleTitleMinimax and fixed point theorems Mathematische Annalen 248 73–77 Occurrence Handle10.1007/BF01349255

    Article  Google Scholar 

  8. I.V. Konnov J.C. Yao (1999) ArticleTitleExistence of solutions for generalized vector equilibrium problems Journal of Mathematical Analysis and Applications 233 328–335 Occurrence Handle10.1006/jmaa.1999.6312

    Article  Google Scholar 

  9. D. Kuroiwa (1996) ArticleTitleConvexity for set-valued maps Applied Mathematics Letter 9 97–101

    Google Scholar 

  10. S.J. Li K.L. Teo X.Q. Yang (2005) ArticleTitleGeneralized vector quasi-equilibrium problems Mathematical Methods of Operations Research 61 3

    Google Scholar 

  11. Li, S.J., Teo, K.L. and Yang, X.Q., On generalized vector quasi-equilibrium problems,preprint.

  12. S.J. Li H. Yan G.Y. Chen (2003) ArticleTitleDifferential and sensitivity properties of gap functions for vector variational inequalities Mathematical Methods of Operations Research 57 377–391

    Google Scholar 

  13. X.Q. Yang (2003) ArticleTitleOn the gap functions of prevariational inequalities Journal of Optimization Theory and Applications 116 437–452 Occurrence Handle10.1023/A:1022422407705

    Article  Google Scholar 

  14. X.Q. Yang J.C. Yao (2002) ArticleTitleGap functions and existence of solutions to set-valued vector variational inequalities Journal of Optimization Theory and Applications 115 407–417 Occurrence Handle10.1023/A:1020844423345

    Article  Google Scholar 

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Correspondence to S. J. Li.

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This research is partially supported by the Postdoctoral Fellowship Scheme of The Hong Kong Polytechnic University and the National Natural Science Foundation of China.

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Li, S.J., Teo, K.L., Yang, X.Q. et al. Gap Functions and Existence of Solutions to Generalized Vector Quasi-Equilibrium Problems. J Glob Optim 34, 427–440 (2006). https://doi.org/10.1007/s10898-005-2193-5

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  • DOI: https://doi.org/10.1007/s10898-005-2193-5

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