Skip to main content

Advertisement

SpringerLink
Log in

Existence of Solutions to Generalized Vector Variational-Like Inequalities

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

This paper deals with some existence theorems for generalized vector variational-like inequalities with set-valued mappings in topological vector spaces. The results presented in this paper generalize and improve some previously known results in the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Giannessi, F.: Theorem of alternative, quadratic program and complementarity problems. In: Cottle, R.W., Giannessi, F., Lions, J.L. (eds.) Variational Inequality and Complementarity Problems, pp. 151–186. Wiley, New York (1980)

    Google Scholar 

  2. Giannessi, F. (ed.): Vector Variational Inequalities and Vector Equilibria, Mathematical Theories. Nonconvex Optimization and Applications, vol. 38. Kluwer Academic, Dordrecht (2000)

    MATH  Google Scholar 

  3. Giannessi, F., Maugeri, A., Pardalos, P.M. (eds.): Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Methods. Nonconvex Optimization and Its Applications, vol. 58. Kluwer Academic, Dordrecht (2001)

    Google Scholar 

  4. Daniele, P., Giannessi, F., Maugeri, A. (eds.): Equilibrium Problems and Variational Models. Including Papers from the Meeting held in Erice, June 23–July 2, 2000. Nonconvex Optimization and Its Applications, vol. 68. Kluwer Academic, Norwell (2003)

    Google Scholar 

  5. Chen, G.-Y., Hou, S.H.: Existence of solutions for vector variational inequalities. In: Giannessi, F. (ed.) Vector Variational Inequalities and Vector Equilibria, Mathematical Theories, pp. 73–86. Nonconvex Optimization and Applications, vol. 38. Kluwer Academic, Dordrecht (2000)

    Google Scholar 

  6. Fang, Y.-P., Huang, N.-J.: Strong vector variational inequalities in Banach spaces. Appl. Math. Lett. 19, 362–368 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. Fang, Y.-P., Huang, N.-J.: Existence results for generalized implicit vector variational inequalities with multivalued mappings. Indian J. Pure Appl. Math. 36, 629–640 (2005)

    MATH  MathSciNet  Google Scholar 

  8. Fang, Y.-P., Huang, N.-J.: Existence results for systems of strong implicit vector variational inequalities. Acta Math. Hung. 103, 265–277 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  9. Kazmi, K.R., Khan, S.A.: Existence of solutions to a generalized system. J. Optim. Theory Appl. 142, 355–361 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  10. Lin, L.-J., Hsu, H.-W.: Existence theorems of systems of vector quasi-equilibrium problems and mathematical programs with equilibrium constraint. J. Glob. Optim. 37, 195–213 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  11. Luc, D.T.: An abstract problem in variational analysis. J. Optim. Theory Appl. 138, 65–76 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  12. Tan, N.X.: Quasi-variational inequalities in topological linear locally convex Hausdorff spaces. Math. Nachr. 122, 231–245 (1985)

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  15. Hadjisavvas, N.: Continuity and maximality properties of pseudomonotone operators. J. Convex Anal. 10, 465–475 (2003)

    MATH  MathSciNet  Google Scholar 

  16. Clarke, F.H., Ledyaev, Yu.S., Stern, R.J., Wolenski, P.R.: Nonsmooth Analysis and Control Theory. Springer, Berlin (1998)

    MATH  Google Scholar 

  17. Yang, X.-Q.: A Hahn-Banach theorem in ordered linear spaces and its applications. Optimization 25, 1–9 (1992)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    A. P. Farajzadeh

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

    A. P. Farajzadeh

  3. Department of Mathematics, University of Shahrekord, Shahrekord, 88186-34141, Iran

    A. Amini-Harandi

  4. Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran, Iran

    A. Amini-Harandi

  5. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

    K. R. Kazmi

Authors
  1. A. P. Farajzadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Amini-Harandi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. R. Kazmi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. R. Kazmi.

Additional information

Communicated by F. Giannessi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Farajzadeh, A.P., Amini-Harandi, A. & Kazmi, K.R. Existence of Solutions to Generalized Vector Variational-Like Inequalities. J Optim Theory Appl 146, 95–104 (2010). https://doi.org/10.1007/s10957-010-9659-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-010-9659-4

Keywords

Search

Navigation