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The Levitin-Polyak well-posedness by perturbations for systems of general variational inclusion and disclusion problems

Author

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  • J. W. Chen

    (Southwest University)

  • Y. J. Cho

    (Gyeongsang National University)

  • S. A. Khan

    (BITS-Pilani, Dubai Campus)

  • Z. Wan

    (Wuhan University)

  • C. F. Wen

    (Kaohsiung Medical University)

Abstract

In this paper, the notions of the Levitin-Polyak well-posedness by perturbations for system of general variational inclusion and disclusion problems (shortly, (SGVI) and (SGVDI)) are introduced in Hausdorff topological vector spaces. Some sufficient and necessary conditions of the Levitin-Polyak well-posedness by perturbations for (SGVI) (resp., (SGVDI)) are derived under some suitable conditions. We also explore some relations among the Levitin-Polyak well-posedness by perturbations, the existence and uniqueness of solution of (SGVI) and (SGVDI), respectively. Finally, the lower (upper) semicontinuity of the approximate solution mappings of (SGVI) and (SGVDI) are established via the Levitin-Polyak well-posedness by perturbations.

Suggested Citation

  • J. W. Chen & Y. J. Cho & S. A. Khan & Z. Wan & C. F. Wen, 2015. "The Levitin-Polyak well-posedness by perturbations for systems of general variational inclusion and disclusion problems," Indian Journal of Pure and Applied Mathematics, Springer, vol. 46(6), pages 901-920, December.
    • Handle: RePEc:spr:indpam:v:46:y:2015:i:6:d:10.1007_s13226-015-0164-1
    DOI: 10.1007/s13226-015-0164-1
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    References listed on IDEAS

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    1. 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.
    2. San-hua Wang & Nan-jing Huang & Donal O’Regan, 2013. "Well-posedness for generalized quasi-variational inclusion problems and for optimization problems with constraints," Journal of Global Optimization, Springer, vol. 55(1), pages 189-208, January.
    3. L. C. Ceng & N. Hadjisavvas & S. Schaible & J. C. Yao, 2008. "Well-Posedness for Mixed Quasivariational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 109-125, October.
    4. S. Al-Homidan & Q. H. Ansari & S. Schaible, 2007. "Existence of Solutions of Systems of Generalized Implicit Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 515-531, September.
    5. S. Li & M. Li, 2009. "Levitin–Polyak well-posedness of vector equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 125-140, March.
    6. 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.
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