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Hölder continuity and upper estimates of solutions to vector quasiequilibrium problems

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Listed:
  • Li, S.J.
  • Chen, C.R.
  • Li, X.B.
  • Teo, K.L.

Abstract

In this paper, we establish the Hölder continuity of solution mappings to parametric vector quasiequilibrium problems in metric spaces under the case that solution mappings are set-valued. Our main assumptions are weaker than those in the literature, and the results extend and improve the recent ones. Furthermore, as an application of Hölder continuity, we derive upper bounds for the distance between an approximate solution and a solution set of a vector quasiequilibrium problem with fixed parameters.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:210:y:2011:i:2:p:148-157
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    References listed on IDEAS

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    1. X. H. Gong, 2008. "Continuity of the Solution Set to Parametric Weak Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 35-46, October.
    2. X. H. Gong & J. C. Yao, 2008. "Lower Semicontinuity of the Set of Efficient Solutions for Generalized Systems," Journal of Optimization Theory and Applications, Springer, vol. 138(2), pages 197-205, August.
    3. K. Kimura & J. C. Yao, 2008. "Semicontinuity of Solution Mappings of Parametric Generalized Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 429-443, September.
    4. 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.
    5. Li, S.J. & Teo, K.L. & Yang, X.Q., 2008. "A remark on a standard and linear vector network equilibrium problem with capacity constraints," European Journal of Operational Research, Elsevier, vol. 184(1), pages 13-23, January.
    6. Li, S.J. & Li, X.B. & Wang, L.N. & Teo, K.L., 2009. "The Hölder continuity of solutions to generalized vector equilibrium problems," European Journal of Operational Research, Elsevier, vol. 199(2), pages 334-338, December.
    7. S.J. Li & G.Y. Chen & K.L. Teo, 2002. "On the Stability of Generalized Vector Quasivariational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 113(2), pages 283-295, May.
    8. Fang, Ya-Ping & Huang, Nan-Jing & Yao, Jen-Chih, 2010. "Well-posedness by perturbations of mixed variational inequalities in Banach spaces," European Journal of Operational Research, Elsevier, vol. 201(3), pages 682-692, March.
    9. 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.
    10. P. Q. Khanh & L. M. Luu, 2007. "Lower Semicontinuity and Upper Semicontinuity of the Solution Sets and Approximate Solution Sets of Parametric Multivalued Quasivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 329-339, June.
    11. Wu Li & Ivan Singer, 1998. "Global Error Bounds for Convex Multifunctions and Applications," Mathematics of Operations Research, INFORMS, vol. 23(2), pages 443-462, May.
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    Cited by:

    1. Yuehu Wang & Baoqing Liu, 2019. "Order-Preservation Properties of Solution Mapping for Parametric Equilibrium Problems and Their Applications," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 881-901, December.
    2. 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.
    3. 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.
    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. 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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