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Vector Equilibrium Problems. Existence Theorems and Convexity of Solution Set

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  • Jun-Yi Fu

Abstract

The natural quasi-concavity of set-valued mappings in an ordered vector space is introduced. Existence theorems for vector equilibrium problems involving set-valued monotone mappings are obtained and the convexity of the solution set is shown. Copyright Springer Science+Business Media New York 2005

Suggested Citation

  • Jun-Yi Fu, 2005. "Vector Equilibrium Problems. Existence Theorems and Convexity of Solution Set," Journal of Global Optimization, Springer, vol. 31(1), pages 109-119, January.
    • Handle: RePEc:spr:jglopt:v:31:y:2005:i:1:p:109-119
    DOI: 10.1007/s10898-004-4274-2
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    Citations

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    Cited by:

    1. X. H. Gong, 2007. "Connectedness of the Solution Sets and Scalarization for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 151-161, May.
    2. Jia-Wei Chen & Zhongping Wan & Yeol Cho, 2013. "Levitin–Polyak well-posedness by perturbations for systems of set-valued vector quasi-equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(1), pages 33-64, February.
    3. Yangdong Xu & Pingping Zhang, 2018. "Connectedness of Solution Sets of Strong Vector Equilibrium Problems with an Application," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 131-152, July.
    4. Adela Elisabeta Capătă, 2024. "Generalized Vector Quasi-Equilibrium Problems," Mathematics, MDPI, vol. 12(6), pages 1-14, March.
    5. Gábor Kassay & Mihaela Miholca & Nguyen The Vinh, 2016. "Vector Quasi-Equilibrium Problems for the Sum of Two Multivalued Mappings," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 424-442, May.
    6. S. Li & H. Liu & Y. Zhang & Z. Fang, 2013. "Continuity of the solution mappings to parametric generalized strong vector equilibrium problems," Journal of Global Optimization, Springer, vol. 55(3), pages 597-610, March.

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