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Journal of Global Optimization

, Volume 57, Issue 4, pp 1401–1418 | Cite as

Continuity of solution mappings in some parametric non-weak vector Ky Fan inequalities

  • Pham Huu SachEmail author
  • Nguyen Ba Minh
Article

Abstract

This paper gives sufficient conditions for the continuity of the solution mappings of parametric non-weak vector Ky Fan inequality problems with moving cones. The main results of the paper are new and are obtained under an assumption different from the known density hypothesis. They are written in terms of nonlinear scalarization functions associated to the data of the problems under consideration. Verifiable conditions are given, and examples are provided.

Keywords

Nonlinear scalarization function Ky Fan inequality  Moving cone  Set-valued map Continuity 

Mathematics Subject Classification

49J53 90C29 90C47 

Notes

Acknowledgments

This research is funded by Vietnam National Foundation for Science and Technology (NAFOSTED) under grant number 101.01-2011.52. The authors would like to thank the referees for their valuable comments.

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Hanoi Institute of MathematicsHanoiVietnam
  2. 2.Hanoi University of CommerceHanoiVietnam

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