Skip to main content
SpringerLink
Log in

Some further generalizations of Ky Fan's minimax inequality and its applications to variational inequalities

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

The purpose of this paper is to introduce the concept of generalized KKM mapping and to obtain some general version of the famous KKM theorem and Ky Fan's minimax inequality. As applications, we utilize the results presented in this paper to study the saddle point problem and the existence problem of solutions for a class of quasi-variational inequalities. The results obtained in this paper extend and improve some recent results of [1–6].

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. Yeh, C.L., A minimax inequalities and its applications to variational inequalities,Pacific J. Math.,97 (1981), 477–480.

    Google Scholar 

  2. Shin, M.H. and K.K. Tan, Generalized quasi-variational inequalities in L.C.S.,J. Math. Anal. Appl.,108 (1985), 333–343.

    Google Scholar 

  3. Zhou, J. X. and G. Chen, Diagonal convexity conditions for problems in convex analysis and quasi-variational inequalities,J. Math. Anal. Appl.,132 (1988), 213–223.

    Google Scholar 

  4. Bardaro, C. and R. Ceppitelli, Some further generalizations of Knaster-Kuratowski-Mazurkiewcz theorem and minimax inequalities,J. Math. Anal. Appl.,132 (1988), 484–490.

    Google Scholar 

  5. Aubin, J.P., and I. Ekeland,Applied Nonlinear Analysis, New York. Wiley-Interscience Publication (1984).

    Google Scholar 

  6. Lassonde, M., On the use of KKM multifunctions in fixed point theory and related topics,J. Math. Anal. Appl.,97 (1985), 151–201.

    Google Scholar 

  7. Zhang Shi-sheng and Shu Yong-lu, Variational inequalities of multivalued mappings and its applications to nonlinear programming and the saddle problem,Acta of Applied Math. (to be published).

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu

    Zhang Shi-Sheng

  2. Department of Mathematics, Yunnan National Institute, Kunming

    Yang Gan-Shan

Authors
  1. Zhang Shi-Sheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yang Gan-Shan
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The project supported by National Natur. Sci. Found. of China

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shi-Sheng, Z., Gan-Shan, Y. Some further generalizations of Ky Fan's minimax inequality and its applications to variational inequalities. Appl Math Mech 11, 1027–1034 (1990). https://doi.org/10.1007/BF02015686

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02015686

Key words

Search

Navigation