Well-posedness for generalized variational-hemivariational inequalities with perturbations in reflexive banach spaces

  • Lu-Chuan Ceng
  • Yung-Yih Lur
  • Ching-Feng Wen
Keywords: Generalized variational-hemivariational inequality, Well-posedness, Clarke's generalized gradient, Approximating sequence, Inclusion problem

Abstract

In this paper, we consider an extension of well-posedness for a minimization problem to a class of generalized variational-hemivariational inequalities with perturbations in reflexive Banach spaces. We establish some metric characterizations for the $\alpha$-well-posed generalized variational-hemivariational inequality and give some conditions under which the generalized variational-hemivariational inequality is strongly $\alpha$-well-posed in the generalized sense. Under some mild conditions, we also prove the equivalence between the $\alpha$-well-posedness of the generalized variational-hemivariational inequality and the $\alpha$-well-posedness of the corresponding inclusion problem.

Author Biographies

Lu-Chuan Ceng
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China.
Yung-Yih Lur
Department of IndustrialManagement, Vanung University, Taoyuan, Taiwan.
Ching-Feng Wen
Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization, KaohsiungMedical University, Kaohsiung, 80708, Taiwan; Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 80708, Taiwan.

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Published
2017-12-30
How to Cite
Ceng, L.-C., Lur, Y.-Y., & Wen, C.-F. (2017). Well-posedness for generalized variational-hemivariational inequalities with perturbations in reflexive banach spaces. Tamkang Journal of Mathematics, 48(4), 345-364. https://doi.org/10.5556/j.tkjm.48.2017.2460
Section
Papers