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On Hölder continuity of solution maps of parametric primal and dual Ky Fan inequalities

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  • L. Anh
  • P. Khanh
  • T. Tam

Abstract

We consider parametric primal and dual Ky Fan inequalities in metric linear spaces. Sufficient conditions for Hölder continuity of solutions are established. Many examples are provided to illustrate the essentialness of the imposed assumptions and advantages of the results over existing ones. As applications, we derive this Hölder continuity of solutions for constrained minimization and variational inequalities. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • L. Anh & P. Khanh & T. Tam, 2015. "On Hölder continuity of solution maps of parametric primal and dual Ky Fan inequalities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 151-167, April.
    • Handle: RePEc:spr:topjnl:v:23:y:2015:i:1:p:151-167
    DOI: 10.1007/s11750-014-0332-1
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    References listed on IDEAS

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    1. I. V. Konnov & S. Schaible, 2000. "Duality for Equilibrium Problems under Generalized Monotonicity," Journal of Optimization Theory and Applications, Springer, vol. 104(2), pages 395-408, February.
    2. L. Q. Anh & P. Q. Khanh, 2009. "Hölder Continuity of the Unique Solution to Quasiequilibrium Problems in Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 37-54, April.
    3. P. Q. Khanh & N. H. Quan, 2011. "Generic Stability and Essential Components of Generalized KKM Points and Applications," Journal of Optimization Theory and Applications, Springer, vol. 148(3), pages 488-504, March.
    4. Lam Anh & Phan Khanh, 2010. "Continuity of solution maps of parametric quasiequilibrium problems," Journal of Global Optimization, Springer, vol. 46(2), pages 247-259, February.
    5. Nguyen Hai & Phan Khanh & Nguyen Quan, 2009. "On the existence of solutions to quasivariational inclusion problems," Computational Optimization and Applications, Springer, vol. 45(4), pages 565-581, December.
    6. S. J. Li & X. B. Li, 2011. "Hölder Continuity of Solutions to Parametric Weak Generalized Ky Fan Inequality," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 540-553, June.
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    Cited by:

    1. Tran Ngoc Tam, 2022. "On Hölder continuity of solution maps to parametric vector Ky Fan inequalities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 77-94, April.

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