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Some equivalence results for well-posedness of hemivariational inequalities

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  • Yi-bin Xiao
  • Xinmin Yang
  • Nan-jing Huang

Abstract

In the present paper, we are devoted to exploring conditions of well-posedness for hemivariational inequalities in reflexive Banach spaces. By using some equivalent formulations of the hemivariational inequality considered under different monotonicity assumptions, we establish two kinds of conditions under which the strong well-posedness and the weak well-posedness for the hemivariational inequality considered are equivalent to the existence and uniqueness of its solution, respectively. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:61:y:2015:i:4:p:789-802
    DOI: 10.1007/s10898-014-0198-7
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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.
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    Cited by:

    1. Savin Treanţă, 2021. "On Well-Posedness of Some Constrained Variational Problems," Mathematics, MDPI, vol. 9(19), pages 1-12, October.
    2. Savin Treanţă, 2022. "Well-Posedness Results of Certain Variational Inequalities," Mathematics, MDPI, vol. 10(20), pages 1-15, October.
    3. Shengda Zeng & Dumitru Motreanu & Akhtar A. Khan, 2022. "Evolutionary Quasi-Variational-Hemivariational Inequalities I: Existence and Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 950-970, June.
    4. Mircea Sofonea & Yi-bin Xiao, 2019. "On the Well-Posedness Concept in the Sense of Tykhonov," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 139-157, October.

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