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Existence of projected solutions for quasi-variational hemivariational inequality

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EN
In this short article, we prove the existence of projected solutions to a class of quasi-variational hemivariational inequalities with non-self-constrained mapping, which generalizes the results of Allevi et al. (Quasi-variational problems with non-self map on Banach spaces: Existence and applications, Nonlinear Anal. Real World Appl. 67 (2022), 103641, DOI: https://doi.org/10.1016/j.nonrwa.2022.103641.)
Wydawca
Rocznik
Strony
art. no. 20230139
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
  • School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, Zhejiang, P.R. China
autor
  • School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, Zhejiang, P.R. China
autor
  • Center for Applied Mathematics of Guangxi, and Guangxi Colleges and Universities, and Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, Guangxi, P.R. China
autor
  • Center for General Education, China Medical University, Taichuug 406040, Taiwan
Bibliografia
  • [1] D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, SIAM, New York, 2000.
  • [2] G. Fichera, Problemi Elastostatici con Vincoli Unilaterali: il Problema di Signorini con Ambigue Condizioni al Contorno, Memorie DellaAccademia Nazionale Dei Lincei, 1964.
  • [3] S. D. Zeng and S. Migórski, Noncoercive hyperbolic variational inequalities with applications to contact mechanics, J. Math. Anal. Appl. 455 (2017), no. 1, 619–637, DOI: https://doi.org/10.1016/j.jmaa.2017.05.072.
  • [4] R. T. Rockafellar and J. Sun, Solving monotone stochastic variational inequalities and complementarity problems by progressive hedging, Math. Program. 174 (2019), no. 1–2, 453–471, DOI: https://doi.org/10.1007/s10107-018-1251-y.
  • [5] D. Chan and J. S. Pang, The generalized Quasi variational inequality problem, Math. Oper. Res. 7 (1982), no. 2, 211–222, DOI: https://doi.org/10.1287/moor.7.2.211.
  • [6] S. D. Zeng, S. Migórski, and A. A. Khan, Nonlinear quasi-hemivariational inequalities: Existence and optimal control, SIAM J. Control Optim. 59 (2021), 1246–1274, DOI: https://doi.org/10.1137/19M1282210.
  • [7] D. Aussel and J. Cotrina, Quasimonotone quasivariational inequalities: Existence results and applications, J. Optim. Theory Appl. 158 (2013), no. 3, 637–652, DOI: https://doi.org/10.1007/s10957-013-0270-3.
  • [8] N. X. Tan, Quasi-variational inequality in topological linear locally convex Hausdorff spaces, Math. Nachr. 122 (1985), no. 1, 231–245, DOI: https://doi.org/10.1002/mana.19851220123.
  • [9] D. Aussel, A. Sultana, and V. Vetrivel, On the existence of projected solutions of quasi-variational inequalities and generalized Nash equilibrium problems, J. Optim. Theory Appl. 170 (2016), no. 3, 818–837, DOI: https://doi.org/10.1007/s10957-016-0951-9.
  • [10] P. Bhattacharyya and V. Vetrivel, An existence theorem on generalized quasi-variational inequality problem, J. Math. Anal. Appl. 188 (1994), no. 2, 610–615, DOI: https://doi.org/10.1006/jmaa.1994.1448.
  • [11] J. Cotrina and J. Zuniga, Quasi-equilibrium problems with non-self constraint map, J. Global Optim. 75 (2019), no. 1, 177–197, DOI: https://doi.org/10.1007/s10898-019-00762-5.
  • [12] E. Allevi, M. E. D. Giuli, M. Milasi, and D. Scopelliti, Quasi-variational problems with non-self map on Banach spaces: Existence and applications, Nonlinear Anal. Real World Appl. 67 (2022), 103641, DOI: https://doi.org/10.1016/j.nonrwa.2022.103641.
  • [13] P. D. Panagiotopoulos, Nonconvex energy functions, hemivariational inequalities and substationary principles, Acta Mech., 42 (1983), no. 3–4, 160–183, DOI: https://doi.org/10.1007/BF01170410.
  • [14] P. D. Panagiotopoulos, Inequality Problems in Mechanics and Applications, Birkhäuser, Boston, 1985.
  • [15] P. D. Panagiotopoulos, Hemivariational Inequalities, Applications in Mechanics and Engineering, Springer-Verlag, Berlin, 1993.
  • [16] W. Han, M. Sofonea, and D. Danan, Numerical analysis of stationary variational-hemivariational inequalities, Numer. Math. 139 (2018), 563–592, DOI: https://doi.org/10.1007/s00211-018-0951-9.
  • [17] S. Migórski, A. Ochal, and M. Sofonea, History-dependent variational-hemivariational inequalities in contact mechanics, Nonlinear Anal. Real World Appl. 22 (2015), 604–618, DOI: https://doi.org/10.1016/j.nonrwa.2014.09.021.
  • [18] Z. H. Liu, Generalized quasi-variational hemi-variational inequalities, Appl. Math. Lett. 17 (2004), no. 6, 741–745, DOI: https://doi.org/10.1016/S0893-9659(04)90115-2.
  • [19] G. J. Tang, X. Wang, and Z. B. Wang, Existence of variational quasi-hemivariational inequalities involving a set-valued operator and a nonlinear term, Optim. Lett. 9 (2015), 75–90, DOI: https://doi.org/10.1007/s11590-014-0739-5.
  • [20] S. Migórski, A. A. Khan, and S. D. Zeng, Inverse problems for nonlinear quasi-hemivariational inequalities with application to mixed boundary value problems, Inverse Problems 36 (2020), no. 2, 024006, DOI: https://doi.org/10.1088/1361-6420/ab44d7.
  • [21] Z. H. Liu, D. Motreanu, and S. D. Zeng, Nonlinear evolutionary systems driven by quasi-hemivariational inequalities, Math. Methods Appl. Sci. 41 (2017), no. 3, 409–421, DOI: https://doi.org/10.1002/mma.4660.
  • [22] M. Lassonde, Fixed points for Kakutani factorizable multifunctions, J. Math. Anal. Appl. 152 (1990), no. 1, 46–60, DOI: https://doi.org/10.1016/0022-247X(90)90092-T.
  • [23] Q. H. Ansari, E. Kobis, and J.-C. Yao, Vector Variational Inequalities and Vector Optimization, Springer, New York, 2018.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-8d69a1df-b845-413c-9207-391046251576
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