Skip to main content

Generalized Vector Variational-Like Inequalities without Monotonicity

  • Chapter
Vector Variational Inequalities and Vector Equilibria

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 38))

Abstract

In this paper, we introduce a class of generalized vector variational-like inequalities without monotonicity which generalizes and unifies generalized vector variational inequalities, vector variational inequalities as well as various extensions of the classic variational inequalities in the literature. Some existence theorems for the generalized vector variational-like inequality without monotonicity are obtained in noncompact setting of topological vector spaces.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aubin J.P. and Ekeland I., “Applied Nonlinear Analysis”. J. Wiley and Sons, New York, 1984

    Google Scholar 

  2. Chen G.-Y., “Existence of solutions for a vector variational inequality: an extension of Hartman-Stampacchia Theorem”. Jou. Optim. Theory Appls., Vol. 74, 1992, pp. 445–456

    Article  MATH  Google Scholar 

  3. Chen G.-Y. and Cheng G.M., “Vector Variational Inequalities and Vector Optimiz.”. Lecture Notes in Econ. and Mathem. System, No. 285, Springer-Verlag, Berlin, 1987, pp. 408–416

    Google Scholar 

  4. Chen G.-Y. and Craven B.D., “Approximate dual and approximate vector variational inequality for multiobjective optimization”. Jou. Austral. Mathem. Soc., ser. A, Vol 47, 1989, pp. 418–423.

    Article  MathSciNet  MATH  Google Scholar 

  5. Chen G.-Y. and Craven B.D., “A vector inequality and optimization over an efficient set”. Zeitschrift für Operations Research, Vol. 3, 1990, pp. 1–12.

    MathSciNet  Google Scholar 

  6. Chen G.-Y. and Yang X.Q., “ The vector complementarity problem and its equivalences with the weak minial element in ordered spaces”. Jou. Mathem. Anal. Appls., Vol. 153, 1990, pp. 136–158.

    Article  MATH  Google Scholar 

  7. Ding X.P. and Tan K.K., “Generalizations of KKM theorem and applications to best approximations and fixed point theorems”. SEA Bull. Mathem., Vol. 17 (2), 1993, pp. 139–150.

    MathSciNet  MATH  Google Scholar 

  8. Giannessi F., “Theorems of the Alternative, Quadratic Programs, and Complementarity Problems.” In “Variational Inequalities and Complementarity Problems”, (Edited by R.W. Cottle, F. Giannessi and J.-L. Lions ), J. Wiley and Sons, New York, 1980, pp. 151–186.

    Google Scholar 

  9. Konnov I.V. and Yao J.C., “On the generalized vector variational inequality problem”. Jou. Mathem. Anal. Appls., Vol. 206, 1997, pp. 42–58.

    Article  MathSciNet  MATH  Google Scholar 

  10. Lai T.C. and Yao J.C., “Existence results for VVIP”. Appls. Mathem. Lett., Vol. 9 (3), 1996, pp. 17–19.

    Article  MathSciNet  MATH  Google Scholar 

  11. Lee G.M., Kim D.S. and Lee B.S., “Generalized vector variational inequality”, Appls. Mathem. Lett., Vol. 9 (1), 1996, pp. 39–42.

    Article  MATH  Google Scholar 

  12. Lee G.M., Kim D.S. and Cho S.J., “ Generalized vector variational inequality and fuzzy extension”, Appls. Mathem. Lett., Vol. 6 (6), 1993, pp. 47–51.

    Article  MathSciNet  MATH  Google Scholar 

  13. Lin K.L., Yang D.P. and Yao J.C., “Generalized vector inequalities”. Jou. Optimiz. Theory Appls., Vol. 92 (1), 1997, pp. 117–125.

    Article  MathSciNet  MATH  Google Scholar 

  14. Parida I., Sahoo M. and Kumar A., “A variational-like inequality problem”. Bull. Austral. M.them. Soc., Vol. 39, 1989, pp. 225–231.

    Article  MathSciNet  MATH  Google Scholar 

  15. Schaefer H.H., “Topological Vector Spaces”. Springer-Verlag, New York, 1971.

    Google Scholar 

  16. Siddiqi A.H., Ansari Q.H. and Khaliq A., “On vector variational inequality”. Jou. Optimiz. Theory Appls., Vol. 84, 1995, pp. 171–180.

    Article  MathSciNet  MATH  Google Scholar 

  17. Yu S.J. and Yao J.C., “On vector variational inequalities”. Jou. Mathem. Anal. Appls., Vol. 89, 1996, pp. 749–769.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Kluwer Academic Publishers

About this chapter

Cite this chapter

Ding, X.P., Tarafdar, E. (2000). Generalized Vector Variational-Like Inequalities without Monotonicity. In: Giannessi, F. (eds) Vector Variational Inequalities and Vector Equilibria. Nonconvex Optimization and Its Applications, vol 38. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0299-5_8

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-0299-5_8

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7985-0

  • Online ISBN: 978-1-4613-0299-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics