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Well-Posedness Results of Certain Variational Inequalities

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  • Savin Treanţă

    (Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
    Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania
    Fundamental Sciences Applied in Engineering—Research Center (SFAI), University Politehnica of Bucharest, 060042 Bucharest, Romania)

Abstract

Well-posedness and generalized well-posedness results are examined for a class of commanded variational inequality problems. In this regard, by using the concepts of hemicontinuity, monotonicity, and pseudomonotonicity of the considered functional, and by introducing the set of approximating solutions of the considered commanded variational inequality problems, we establish several well-posedness and generalized well-posedness results. Moreover, some illustrative examples are provided to highlight the effectiveness of the results obtained in the paper.

Suggested Citation

  • Savin Treanţă, 2022. "Well-Posedness Results of Certain Variational Inequalities," Mathematics, MDPI, vol. 10(20), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3809-:d:943325
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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. 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.
    3. M. B. Lignola, 2006. "Well-Posedness and L-Well-Posedness for Quasivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 119-138, January.
    4. Laura Scrimali, 2008. "The financial equilibrium problem with implicit budget constraints," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 191-203, June.
    5. Shu Lv & Yi-bin Xiao & Zhi-bin Liu & Xue-song Li, 2012. "Well-Posedness by Perturbations for Variational-Hemivariational Inequalities," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-18, August.
    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.
    7. Yi-bin Xiao & Xinmin Yang & Nan-jing Huang, 2015. "Some equivalence results for well-posedness of hemivariational inequalities," Journal of Global Optimization, Springer, vol. 61(4), pages 789-802, April.
    8. Stella Dafermos, 1980. "Traffic Equilibrium and Variational Inequalities," Transportation Science, INFORMS, vol. 14(1), pages 42-54, February.
    9. Smith, M. J., 1979. "The existence, uniqueness and stability of traffic equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 13(4), pages 295-304, December.
    10. Yi-bin Xiao & Nan-jing Huang, 2011. "Well-posedness for a Class of Variational–Hemivariational Inequalities with Perturbations," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 33-51, October.
    11. Shengda Zeng & Emilio Vilches, 2020. "Well-Posedness of History/State-Dependent Implicit Sweeping Processes," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 960-984, September.
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