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Hölder Continuity of the Unique Solution to Quasiequilibrium Problems in Metric Spaces

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  • L. Q. Anh

    (Cantho University)

  • P. Q. Khanh

    (International University of Hochiminh City)

Abstract

We extend and sharpen the result in Ait Mansour and Scrimali (J. Glob. Optim. 40:175–184, 2008) on the Hölder continuity of the solution sets of quasivariational inequalities in Hilbert spaces to the case of quasiequilibrium problems in metric spaces. Applications to some important problems are also provided.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:141:y:2009:i:1:d:10.1007_s10957-008-9508-x
    DOI: 10.1007/s10957-008-9508-x
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    References listed on IDEAS

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    1. Goh, C. J. & Yang, X. Q., 1999. "Vector equilibrium problem and vector optimization," European Journal of Operational Research, Elsevier, vol. 116(3), pages 615-628, August.
    2. L. Q. Anh & P. Q. Khanh, 2007. "On the Stability of the Solution Sets of General Multivalued Vector Quasiequilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 135(2), pages 271-284, November.
    3. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    4. Smith, M. J., 1979. "The existence, uniqueness and stability of traffic equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 13(4), pages 295-304, December.
    5. N. X. Hai & P. Q. Khanh, 2007. "Existence of Solutions to General Quasiequilibrium Problems and Applications," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 317-327, June.
    6. X. Q. Yang & C. J. Goh, 1997. "On Vector Variational Inequalities: Application to Vector Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 95(2), pages 431-443, November.
    7. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    8. P. Q. Khanh & L. M. Luu, 2004. "On the Existence of Solutions to Vector Quasivariational Inequalities and Quasicomplementarity Problems with Applications Break to Traffic Network Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 533-548, December.
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    Cited by:

    1. Yu Han, 2018. "Lipschitz Continuity of Approximate Solution Mappings to Parametric Generalized Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 763-793, September.
    2. 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.
    3. 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.
    4. Li, X.B. & Li, S.J., 2014. "Hölder continuity of perturbed solution set for convex optimization problems," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 908-918.
    5. L. Anh & A. Kruger & N. Thao, 2014. "On Hölder calmness of solution mappings in parametric equilibrium problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 331-342, April.
    6. Massimiliano Giuli, 2013. "Closedness of the Solution Map in Quasivariational Inequalities of Ky Fan Type," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 130-144, July.
    7. X. B. Li & X. J. Long & J. Zeng, 2013. "Hölder Continuity of the Solution Set of the Ky Fan Inequality," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 397-409, August.
    8. Li, S.J. & Chen, C.R. & Li, X.B. & Teo, K.L., 2011. "Hölder continuity and upper estimates of solutions to vector quasiequilibrium problems," European Journal of Operational Research, Elsevier, vol. 210(2), pages 148-157, April.
    9. 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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