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Locally Densely Defined Equilibrium Problems

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Abstract

In this paper, by an approach, which is based on a notion of sequentially sign property for bifunctions, we establish existence results for equilibrium problems in the setting of Hausdorff locally convex topological vector spaces. The main advantages of this approach are that our conditions are imposed just on a locally segment-dense set, instead of the whole domain.

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References

  1. Fan, K.: A minimax inequality and applications. In: Shisha, O. (ed.) Inequalities III, pp. 103–113. Academic Press, New York (1972)

    Google Scholar 

  2. Muu, L.D., Oettli, W.: Convergence of an adaptive penalty scheme for finding constrained equilibria. Nonlinear Anal. 18, 1159–1166 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  3. Blum, E., Oettli, W.: From optimization and variational inequalities to equilibrium problems. Math. Stud. 63, 123–145 (1994)

    MathSciNet  MATH  Google Scholar 

  4. Bigi, G., Castellani, M., Pappalardo, M., Passacantando, M.: Existence and solution methods for equilibria. Eur. J. Oper. Res. 227, 1–11 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bianchi, M., Pini, R.: Coercivity conditions for equilibrium problems. J. Optim. Theory Appl. 124, 79–92 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bianchi, M., Pini, R.: A note on equilibrium problems with properly quasimonotone bifunctions. J. Glob. Optim. 20, 67–76 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bianchi, M., Schaible, S.: Generalized monotone bifunctions and equilibrium problems. J. Optim. Theory Appl. 90, 31–43 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bigi, G., Castellani, M., Kassay, G.: A dual view of equilibrium problems. J. Math. Anal. Appl. 342, 17–26 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Burachik, R., Kassay, G.: On a generalized proximal point method for solving equilibrium problems in Banach spaces. Nonlinear Anal. 75, 6456–6464 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. Giannessi, F.: Vector Variational Inequalities and Vector Equilibria. Mathematical Theories. Kluwer Academic Publishers, Dordrecht (2000)

    Book  MATH  Google Scholar 

  11. Iusem, A.N., Kassay, G., Sosa, W.: On certain conditions for the existence of solutions of equilibrium problems. Math. Prog. 116, 259–273 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Iusem, A.N., Sosa, W.: New existence results for equilibrium problems. Nonlinear Anal. 52, 621–635 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  13. László, S., Viorel, A.: Densely defined equilibrium problems. J. Optim. Theory Appl. 166, 52–75 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  14. Alleche, B., Rǎdulescu, V.D.: Set-valued equilibrium problems with applications to Browder variational inclusions and to fixed point theory. Nonlinear Anal. Real World Appl. 28, 251-68 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  15. Aussel, D., Hadjisavvas, N.: On quasimonotone variational inequalities. J. Optim. Theory Appl. 121, 445–450 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  16. Castellani, M., Giuli, M.: Refinements of existence results for relaxed quasimonotone equilibrium problem. J. Glob. Optim. 57, 1213–1227 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  17. Farajzadeh, A.P., Zafarani, J.: Equilibrium problems and variational inequalities in topological vector spaces. Optimization 59, 485–499 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  18. Jafari, S., Farajzadeh, A.P.: Existence results for equilibrium problems under strong sign property. Int. J. Nonlinear Anal. Appl. (2016) (accepted manuscript)

  19. Luc, D.T.: Existence results for densely pseudomonotone variational inequalities. J. Math. Anal. Appl. 254, 291–308 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  20. Alleche, B., Rǎdulescu, V.D., Sebaoui, M.: The Tikhonov regularization for equilibrium problems and applications to quasihemivariational inequalities. Optim. Lett. 9, 483–503 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  21. Jahn, J.: Vector Optimization. Springer, New York (2004)

    Book  MATH  Google Scholar 

  22. Karamardian, S.: Strictly quasi-convex (concave) functions and duality in mathematical programming. J. Math. Anal. Appl. 20, 344–358 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  23. Fan, K.: A generalization of Tychonoff’s fixed point theorem. Math. Ann. 142, 305–310 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  24. Fan, K.: Some properties of convex sets related to fixed point theorems. Math. Ann. 266, 519–537 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  25. Luc, D.T., Sarabi, E., Soubeyran, A.: Existence of solutions in variational relation problems without convexity. J. Math. Anal. Appl. 364, 544–555 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  26. Tian, G.Q.: Generalizations of the FKKM theorem and the Ky Fan minimax inequality, with applications to maximal elements, price equilibrium, and complementarity. J. Math. Anal. Appl. 170, 457–471 (1992)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

The authors would like to thank Prof. Dinh The Luc for taking time to read the paper and his valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Razi University, Kermanshah, 67149, Iran

    Somaye Jafari & Ali Farajzadeh

  2. Department of Mathematics, Faculty of Science, Arak University, Arak, 38156-8-8349, Iran

    Sirous Moradi

Authors
  1. Somaye Jafari
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  2. Ali Farajzadeh
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  3. Sirous Moradi
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Corresponding authors

Correspondence to Somaye Jafari or Ali Farajzadeh.

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Communicated by Byung-Soo Lee.

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Jafari, S., Farajzadeh, A. & Moradi, S. Locally Densely Defined Equilibrium Problems. J Optim Theory Appl 170, 804–817 (2016). https://doi.org/10.1007/s10957-016-0950-x

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  • DOI: https://doi.org/10.1007/s10957-016-0950-x

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