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

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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.

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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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Authors and Affiliations

  1. Hanoi Institute of Mathematics, 18 Hoang Quoc Viet Road, 10307 , Hanoi, Vietnam

    Pham Huu Sach

  2. Hanoi University of Commerce, Hanoi, Vietnam

    Nguyen Ba Minh

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  1. Pham Huu Sach
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  2. Nguyen Ba Minh
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Correspondence to Pham Huu Sach.

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Sach, P.H., Minh, N.B. Continuity of solution mappings in some parametric non-weak vector Ky Fan inequalities. J Glob Optim 57, 1401–1418 (2013). https://doi.org/10.1007/s10898-012-0015-0

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