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Variational relation problems and equivalent forms of generalized Fan-Browder fixed point theorem with applications to Stampacchia equilibrium problems

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Abstract

In this paper, we study the existence theorems of solution for variational relation problems. From the existence theorems of solution for variational relation problems, we study equivalent forms of generalized Fan-Browder fixed point theorem, existence theorems of solutions for Stampacchia vector equilibrium problems and generalized Stampacchia vector equilibrium problems. Our results contains many orginal results and have many applications in Nonlinear Analysis.

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References

  1. Browder F.E.: The fixed point theory of multi-valued mappings in topological vector spaces. Math. Ann. 177, 283–301 (1968)

    Article  Google Scholar 

  2. Yuan G.X.Z.: KKM theory and applications in Nonlinear Anlayais. Marcel Dekker Inc., New York (1999)

    Google Scholar 

  3. Lin L.J., Tu C.I.: The studies of variational inclusions problems and variational disclusions problems with applications. Nonlinear Anal. TMA 69, 1981–1998 (2008)

    Article  Google Scholar 

  4. Lin L.J., Chuang C.S.: Systems of nonempty intersection theorems with applications. Nonlinear Anal. TMA 69, 4063–4073 (2008)

    Article  Google Scholar 

  5. Blum E., Oettli W.: From optimization and variational inequalities to equilibrium problems. Math. Student 63, 123–146 (1994)

    Google Scholar 

  6. Luc D.T.: An abstract problem in variational analysis. J. Optim. Theory Appl. 138, 65–78 (2008)

    Article  Google Scholar 

  7. Luc D.T., Sarabi E., Soubeyran A.: Existence of solutions in variational relations without convexity. J. Math. Anal. Appl. 384, 544–555 (2010)

    Article  Google Scholar 

  8. Lin L.J., Anasri Q.H.: Systems of variational relation problems with applications. Nonlinear Anal. 72, 1210–1220 (2010)

    Article  Google Scholar 

  9. Lin L.J., Wang S.Y.: Simultaneous variational relations problems and related applications. Comput. Math. Appl. 58, 1711–1721 (2009)

    Article  Google Scholar 

  10. Balaj M., Lin L.J.: Equivalent forms of generalized KKM theorem and their applications. Nonlinear Anal. 23, 673–682 (2010)

    Google Scholar 

  11. Balaj M., Lin L.J.: Variational relation problems with applications. J. Optim. Theory Appl. 148, 1–13 (2011)

    Article  Google Scholar 

  12. Fu J.Y.: Stampacchia generalized vector quasi-equilibrium problem and vector saddle points. J. Optim. Theory Appl. 128, 259–268 (2006)

    Article  Google Scholar 

  13. Wang S.H., Fu J.Y.: Stampacchia generalized vector quasi-equilibrium problems with set-valued mapping. J. Glob. Optim. 44, 99–110 (2009)

    Article  Google Scholar 

  14. Lin L.J., Yu Z.T., Kassay G.: Eixstence of equilibrium for multivalued mappings and its applications to vector equilibria. J. Optim. Theory Appl. 134, 189–208 (2002)

    Article  Google Scholar 

  15. Lin L.J., Chuang C.S., Wang S.Y.: From quasivariational inclusion problems to Stampacchia vector quasiequilibrium problems., Stampacchia set-valued vector Ekeland’s variational principle and Caristi’s fixed point theorem, nonlinear analysis, theory. Methods Appl. 71, 179–185 (2009)

    Google Scholar 

  16. Pardalos, P.M., Rassias, T.M., Khan, A.A.: Nonlinear Analysis and Variational Problems in Honor of George Isac. Series: Springer Optimization and its Applications, Vol. 35, Springer (2010)

  17. Giannessi, F., Pardalos, M A., Panos, M.: Equilibrium Problems:Nonsmooth Optimization and Variational Inequality Models. Series: Nonconvex Optimization and Its Applications, Vol. 58, Springer (2002)

  18. Maugeri, A., Raciti, F.: On general infinite diminsenal complementarity problems. Optim. Lett. 2 (2008)

  19. Lalitha C.S.: A note on duality of generalized equilibrium problem. Optim. Lett. 4, 57–66 (2010)

    Article  Google Scholar 

  20. Aubin J.P., Cellina A.: Differential inclusions. Springer, Heidelberg (1941)

    Google Scholar 

  21. Ferro F.: A minimax theorem for vector-valued functions. J. Optim. Theory Appl. 60, 19–31 (1989)

    Article  Google Scholar 

  22. Tan N.X.: Quasi-variational inequalities in linear locally convex Hausdorff spaces. Math. Nach. 122, 231–245 (1995)

    Article  Google Scholar 

  23. Lin L.J.: Applications of a fixed point theorem in G-convex space. Nonlinear Anal. 46, 601–608 (2001)

    Article  Google Scholar 

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  1. Department of Mathematics, National Changhua University of Education, Changhua, 50058, Taiwan

    Lai-Jiu Lin

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  1. Lai-Jiu Lin
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Lin, LJ. Variational relation problems and equivalent forms of generalized Fan-Browder fixed point theorem with applications to Stampacchia equilibrium problems. J Glob Optim 53, 215–229 (2012). https://doi.org/10.1007/s10898-011-9676-3

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  • DOI: https://doi.org/10.1007/s10898-011-9676-3

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