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Vector Quasi-Equilibrium Problems for the Sum of Two Multivalued Mappings

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Listed:
  • Gábor Kassay

    (Babeş-Bolyai University)

  • Mihaela Miholca

    (Technical University of Cluj-Napoca)

  • Nguyen The Vinh

    (University of Transport and Communications)

Abstract

In this paper, we study vector quasi-equilibrium problems for the sum of two multivalued bifunctions. The assumptions are required separately on each of these bifunctions. Sufficient conditions for the existence of solutions of such problems are shown in the setting of topological vector spaces. The results in this paper unify, improve and extend some well-known existence theorems from the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:169:y:2016:i:2:d:10.1007_s10957-016-0919-9
    DOI: 10.1007/s10957-016-0919-9
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    References listed on IDEAS

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    1. K. R. Kazmi & S. A. Khan, 2009. "Existence of Solutions to a Generalized System," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 355-361, August.
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    3. D. Chan & J. S. Pang, 1982. "The Generalized Quasi-Variational Inequality Problem," Mathematics of Operations Research, INFORMS, vol. 7(2), pages 211-222, May.
    4. 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.
    5. Yannelis, Nicholas C. & Prabhakar, N. D., 1983. "Existence of maximal elements and equilibria in linear topological spaces," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 233-245, December.
    6. Tian, Guoqiang, 1994. "Generalized KKM theorem, minimax inequalities and their applications," MPRA Paper 41217, University Library of Munich, Germany.
    7. Werner Oettli & Dirk Schläger, 1998. "Existence of equilibria for monotone multivalued mappings," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 219-228, November.
    8. Qamrul Hasan Ansari & Jen-Chih Yao, 2010. "Systems of Vector Quasi-equilibrium Problems and Their Applications," Springer Optimization and Its Applications, in: Regina S. Burachik & Jen-Chih Yao (ed.), Variational Analysis and Generalized Differentiation in Optimization and Control, pages 1-42, Springer.
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    Cited by:

    1. Mircea Balaj, 2021. "Intersection theorems for generalized weak KKM set‐valued mappings with applications in optimization," Mathematische Nachrichten, Wiley Blackwell, vol. 294(7), pages 1262-1276, July.

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