Skip to main content
SpringerLink
Log in

On a Geometric Lemma and Set-Valued Vector Equilibrium Problem

  • Conference paper
Optimization and Control with Applications

Part of the book series: Applied Optimization ((APOP,volume 96))

  • 2490 Accesses

Abstract

Based on a variation of Fan's geometric lemma, an existence theorem of solutions for set-valued vector equilibrium problem is given in this paper.

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

Access this chapter

Log in via an institution
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

  • Kakutani, S. (1941), A generalization of Brouwer's fixed point theorem, Duke Math. Journal, Vol. 8, pp. 457–459.

    Article  MATH  MathSciNet  Google Scholar 

  • Fan, K. (1961), A generalization of Tychonoff's fixed point theorem, Math. Ann., Vol. 142, pp. 305–310.

    Article  MATH  MathSciNet  Google Scholar 

  • Takahashi, W. (1976), Nonlinear variational inequalities and fixed point theorems, J. of Math. Soc. of Japan, Vol. 28, No. 1, pp. 168–181.

    Article  MATH  Google Scholar 

  • Ha, C.W. (1980), Minimax and fixed point theorems, Math. Ann., Vol. 248, pp. 73–77.

    Article  MATH  MathSciNet  Google Scholar 

  • Tian, G. (1992), Generalizations of the FKKM theorem and the Ky Fan minimax inequality, with applications to maximal elements, price equilibrium and complementarity, Journal of Mathematical Analysis and Applications, Vol. 170, No. 2, pp. 457–471.

    Article  MATH  MathSciNet  Google Scholar 

  • Blum, E. and Oettli, W. (1994), ¿From optimization and variational inequalities to equilibrium problems, The Math. Student, Vol. 63, pp.123–145.

    MathSciNet  MATH  Google Scholar 

  • Kuroiwa, D. (1996), Convexity for set-valued maps, Applied Mathematics Letter, Vol. 9, No. 2, pp. 97–101.

    Article  MATH  MathSciNet  Google Scholar 

  • Giannessi, F., Editor (2000), Vector Variational Inequalities and Vector Equilibria: Mathematical Theories, Kluwer Academic Publishers, Dordrecht, The Netherlands.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong

    Shui-Hung Hou

Authors
  1. Shui-Hung Hou
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. The Hong Kong Polytechnic University, Hong Kong

    Liqun Qi , Koklay Teo  & Xiaoqi Yang ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer Science+Business Media, Inc.

About this paper

Cite this paper

Hou, SH. (2005). On a Geometric Lemma and Set-Valued Vector Equilibrium Problem. In: Qi, L., Teo, K., Yang, X. (eds) Optimization and Control with Applications. Applied Optimization, vol 96. Springer, Boston, MA. https://doi.org/10.1007/0-387-24255-4_25

Download citation

Publish with us

Policies and ethics

Search

Navigation