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On Hölder continuity of solution maps to parametric vector Ky Fan inequalities

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  • Tran Ngoc Tam

    (Can Tho University)

Abstract

In this paper, we first introduce the notion of strong quasiconvexity of a vector-valued map. Then, this new condition is utilized to study the existence and stability of solutions to parametric vector Ky Fan inequalities. Namely, sufficient conditions for the nonemptiness of solutions and the Hölder continuity of solution maps to parametric vector Ky Fan inequalities are established. The results obtained in this paper are improvements of the previous ones. At the end of the paper, applications of the main results are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:topjnl:v:30:y:2022:i:1:d:10.1007_s11750-021-00602-4
    DOI: 10.1007/s11750-021-00602-4
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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. 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. 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.
    6. Bin Chen & Nan-jing Huang, 2013. "Continuity of the solution mapping to parametric generalized vector equilibrium problems," Journal of Global Optimization, Springer, vol. 56(4), pages 1515-1528, August.
    7. L. Anh & P. Khanh & T. Tam, 2015. "Erratum to: 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(2), pages 617-617, July.
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