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New Scalarizing Approach to the Stability Analysis in Parametric Generalized Ky Fan Inequality Problems

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Abstract

This paper gives sufficient conditions for the upper and lower semicontinuities of the solution mapping of a parametric mixed generalized Ky Fan inequality problem. We use a new scalarizing approach quite different from traditional linear scalarization approaches which, in the framework of the stability analysis of solution mappings of equilibrium problems, were useful only for weak vector equilibrium problems and only under some convexity and strict monotonicity assumptions. The main tools of our approach are provided by two generalized versions of the nonlinear scalarization function of Gerstewitz. Our stability results are new and are obtained by a unified technique. An example is given to show that our results can be applied, while some corresponding earlier results cannot.

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Acknowledgements

The authors would like to thank the referees for their suggestions, which improved the paper.

The support of The National Foundation for Science and Technology Development, Vietnam, is gratefully acknowledged.

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Authors and Affiliations

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

    Pham Huu Sach

  2. Nong Lam University, Ho Chi Minh City, Vietnam

    Le Anh Tuan

  3. Ninh Thuan College of Pedagogy, Ninh Thuan, Vietnam

    Le Anh Tuan

Authors
  1. Pham Huu Sach
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  2. Le Anh Tuan
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Correspondence to Pham Huu Sach.

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Communicated by Qamrul Hasan Ansari.

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Sach, P.H., Tuan, L.A. New Scalarizing Approach to the Stability Analysis in Parametric Generalized Ky Fan Inequality Problems. J Optim Theory Appl 157, 347–364 (2013). https://doi.org/10.1007/s10957-012-0105-7

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  • DOI: https://doi.org/10.1007/s10957-012-0105-7

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