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

Lu-Chuan Ceng, Yung-Yih Lur, Ching-Feng Wen

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.

Keywords


Generalized variational-hemivariational inequality; Well-posedness; Clarke's generalized gradient; Approximating sequence; Inclusion problem

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References


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DOI: http://dx.doi.org/10.5556/j.tkjm.48.2017.2460

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