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Existence theorems of the hemivariational inequality governed by a multi-valued map perturbed with a nonlinear term in Banach spaces

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  • Rabian Wangkeeree
  • Pakkapon Preechasilp

Abstract

In this paper, we establish some existence results for the hemivariational inequality governed by a multi-valued map perturbed with a nonlinear term in reflexive Banach spaces. Using the concept of the stable $$f$$ -quasimonotonicity, the properties of Clarke’s generalized directional derivative, Clarke’s generalized gradient and KKM technique, some existence theorems of solutions are proved when the constrained set is nonempty, bounded (or unbounded), closed and convex. Our main results extend various results existing in the current literatures. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Rabian Wangkeeree & Pakkapon Preechasilp, 2013. "Existence theorems of the hemivariational inequality governed by a multi-valued map perturbed with a nonlinear term in Banach spaces," Journal of Global Optimization, Springer, vol. 57(4), pages 1447-1464, December.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:4:p:1447-1464
    DOI: 10.1007/s10898-012-0018-x
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    References listed on IDEAS

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    1. Nicuşor Costea & Vicenţiu Rădulescu, 2012. "Inequality problems of quasi-hemivariational type involving set-valued operators and a nonlinear term," Journal of Global Optimization, Springer, vol. 52(4), pages 743-756, April.
    2. D. T. Peng & J. Yu & N. H. Xiu, 2012. "Generic Uniqueness of Solutions for a Class of Vector Ky Fan Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 165-179, October.
    3. S. J. Li & Z. M. Fang, 2010. "Lower Semicontinuity of the Solution Mappings to a Parametric Generalized Ky Fan Inequality," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 507-515, December.
    4. Zijia Peng & Zhenhai Liu, 2011. "Evolution hemivariational inequality problems with doubly nonlinear operators," Journal of Global Optimization, Springer, vol. 51(3), pages 413-427, November.
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    Cited by:

    1. Bijaya Kumar Sahu & Ouayl Chadli & Ram N. Mohapatra & Sabyasachi Pani, 2020. "Existence Results for Mixed Equilibrium Problems Involving Set-Valued Operators with Applications to Quasi-Hemivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 810-823, March.

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